That´s what I´m talking about.
My hands doesn´t feel the same when I practice HS than HT.
Should I practice HS until each hand gets automatic, and then coordinate both together?
First, your hands doesn't feel the same when you practice HS than HT because many "first" wrong movement are lately discarded and so you don't use them anymore when practicing HT, so they will always fell different
Second hands shouldn't get automatic
I mean, that is hands memory and it's good to use it but it's not wise to rely on it
Also, your hands feel different from HT than HS because of brain neurological coordination
You feel more sensitivity in the hand when you use only one and less sensitivty when your brain has to use both
It also depend what side of your brain is more utilized
Another reason why you may feel so much different is tempo and rythm
If you doesn't play at tempo and following the rythm you may notice that you have played notes where actually they shouldn't be played
In this it becomes hard to coordinate both hands because the two lines doesn't coincide (in your mind) since you've practiced with the wrong rythm HS and now the two lines are not coordinated
The solution to this is to work out all rythm problems before ever attempting to play a note of the piece you're studying
Separate each part and clap the whole rythm
When you practice count aloud
I don't think "without thinking" is a good mark for telling that you have learned a piece
You're imho relying too much on muscle memory
Learning a piece well doesn't mean that you play and move your hand without thinking but that your brain think ahead of the fingers and the arms
So you must think must faster
If you just let your hands find their movements without thinking then you're completely relying on hand memory but this is not enough and hands memory is quickly forgotten
So, you shouldn't get your hands HS automized before you can coordinate them together
You must first work out all the rythm problems before playing even a note
Then you mark all those part that are harder or that need a tecnique you don't have yet aquired
So if in a whole sonata there's only a fast thirds 2 bars and a fast cromatic scale 4 bars you just have to work on these section before playing the whole piece
During your practice you're working for two reason
1) teaching the hands new movements
2) training the brain to think ahead of the fingers
So, start only working on these sections
Have many short practice session every day
So work on the first hard section for 15 minutes and then have a 10 minutes pause and work on the other hard section
Remember that the piece must "grow" alone into you
So you practice something and then let it be learned by your unconscious
This is something that every teacher at my school know and I've yet to meet a teacher who doesn't know that a piece improves alone after you've practiced it
So, start with one hand and as soon as it is tired start with other hand
Let say you have a fast scale of 1 bar
You repeat it enough times by alternating slow and fast motions
Slow motions are needed for accuracy, learning the notes and training your brain to think ahead
Fast motions are needed for checking what movements are better at that speed and to then use these movements at slow motions
So, it work like this for me
You repeat the same bar alternating the speed
50 bpm some errors
120 bpm a lot of errors
50 bpm know it's good
55 bpm some errors
120 bpm better than before
55 bpm perfect
120 bpm still a mess
60 bpm good
65 bpm many errors
120 bpm less errors
65 bpm perfect
70 bpm good
120 bpm now it's okay
100 bpm good
120 bpm perfect
You keep alternating the hands so they don't tire
So, let's say know your hands have learned movements needed for fast speed in both HS
Now you can attemp to play these section hand together
Is it's a mees you need more work on these section HS if it's quite good you can practice HT for sometime and then come back to HS
Now you need a way to join all the sections
Te best way is to moving quickly from section to section but waiting some second on the note before playing it
In this way you teach your big muscles and your body how to move and once you have got the big movements properly the littler fingers movements are easier to add
Another think you should do is "penetrating" the piece structure
This means that you change the nature of the piece and in this way you get more recognition of it
So you can change the rythm and using a napoletan, or alla lombarda rythm in these sections
You can play the notes backward
You can play two note, the pause, then another two notes
You can play the section by thirds
Let's say that you drink a cup of hot water and it feels like really hot
The you drink a cup of hottier water
This time the first cup will fell like colder
This is way alternating it works
Anatomically, mentally and neurologically you practice on the piano because you need to teach your hands new movements, to teach your brain to think ahead of your muscles, to have your brain send neurological messages to your arms as fast as possible to teach your brain to coordinate your hands together
Now, both HS and HT, slow motions and fast motions, bar-by-bar and whole are needed but each of one is needed for different reason
By alternating the different kind of brain-thoughts and movements you're sure to get what each of this practice has to offer
Once these sections are okay hands separated (the next days) you can start playing the whole piece (each bar quite fast but waiting on the note on the next bar before playing it)
If the whole piece if okay hands separated you can start practicing hands together seriously; but remember that you already used HT in your alternations
By the whole okay hands separated I mean
1) your brain know the rythm and different rythm of each had and can follow it easily
2) all the movements have been aquired by your hands so when needed you can use them (hence you keep thinking it's not something automatic)
3) you're relaxed and the big muscles moves properly from bar to bar and the fingers movement easily follow the big movements
4) your brain think many bars ahead of your fingers
5) both part are musicallt correct
So as you can see this is a conscoius work not an automatic one
At this point join the hands and play the whole piece (fast but waiting on the first note of each bar before playing it)
mark those piece where the coordination is not okay
Now work only on these section
Alternating HT to HS, alternating slow motions to fast motions and always training your big muscles before the fingers
In fact the most important thing is that you're able to move smoothly from bar to bar .. then you can easily on each bar content
Remember to always clap the whole piece before playing it and if after the work your hands are still not coordinated check if there a rythm problem to work out
So let's say you study a little easy piece such as the Clementi Sonatina n1 op. 36
1) Work out any rythm problem before playing a note
Clap the rythm
Count the rythm
Mark the hard or tecnique demanding parts
2) Work only on those hard section
Work on each section for a 15-20 minutes practice then forget about it until the next day
3) While working on the hard section count the rythm
Alternate left hand and right hand
Alternate HS to HT
(HS to work on each hand HT to check is the work done HS has worked and also to make the brain and the hands relax more from passing to HT to HS)
Alternate slow motions and fast motions
Slow motions to learn the notes, trainining the brain to think ahead and accuracy
Fast motion to check what movements works at speed and what don't work
Work before on the big muscles training them to move smoothly (by moving the hand quickly but waiting on the note before playing it)
4) Join the hard section to the other section to form the whole piece
5) When the piece is learned HS and both hands knwo their part check the rythm problem to work out HT and mark the harder section
6) Work on the harder sections HT the same way you work HS as in point three
7) At this point when speed and tecnique is aquired and all the bar are difficult or easy in the same manner start connection HT all the sections to form the whole piece

Work on the big muscles first and then on the fingers
9) Play each bar fast but moving quickly from bar to bar wait on the first note of each bar before playing it
Remember that when a bar or a section is harder you must analize the reason why:
Is it a rythm problem ?
Is it a wrist angle problem ?
Is it a relaxation problem ?
Is it that my mind is too worried and my inned voice doesn't shut up ?
Is it that I used a wrong fingering ?
Before practicing an hard section understand what you should do to make it easy and what the problem is
Hope this helps
Daniel