There are many ways to improve the left hand (or the right, if that is your weak hand).
However from your description it would seem that your problem is one of co-ordination, since you say that you can play hands separately without problems.
Typically co-ordination problems stem from one hand moving in sympathy with the other. The way to stop this is through nerve inhibition (rather than muscle tension). How do you go about it?
First make sure that your hands separate is immaculate. You should be at the stage where your fingers move automatically and subconsciously (HS), if you have to think about where your hands go next, you are not yet ready for my suggestion below. So keep working on HS until you are confident you can do it in your sleep.
Now try this. I call it “dropping notes”. Select a passage not too large (3 or 4 bars, say), or better still a phrase that makes musical sense.
Start with the right hand. Play the passage/phrase with the right hand not too fast, but not too slow either. Your aim is to keep the right hand going no matter what. You should be able to have a smooth, flowing and even rendition of the right hand.
Now “drop” (i.e. play) the first note of the left hand, as the right hand goes about its business. At this stage it is all right to make mistakes on the left hand. but the right hand must be absolutely perfect. And no matter what happens to the left hand, the right hand must keep going in perfect form all the way to the end of the passage. You are basically familiarising yourself with the “drop” of the left hand while maintaining the right hand going. After a few repeats you should get the hand of it. Now aim to get that first LH note right.
Once you are satisfied that your hands are co-ordinated and yet independent, drop the second LH note. Again, do not worry too much with mistakes on the Left hand, but make sure that the right hand is spotless. No matter what happens the right hand must keep going. Then concentrate on getting the LH flawless.
Keep adding notes on the LH until you complete the passage. Select a passage that is small enough to allow you to complete it in a short time, say 20 minutes. Concentrate completely in getting the RH going perfectly in spite of what may be happening to the Left hand.
Once you complete the passage, you must repeat the whole procedure, but this time in reverse, i.e., start by playing the whole of the LH flawlessly, and drop the RH notes one by one as above. Again, concentrate in making sure that no matter what is happening with the RH, the LH keeps going without mistakes and perfectly.
At the end, the passage should be perfect.
Now move on to the next passage/phrase.
By the way, do not apply this to the whole piece, just to the most difficult parts, or to the parts that are giving you trouble. You may find that mastering the most difficult parts usually results in mastering the easiest parts without any need to work on them.
I hope this helps.
Best wishes,
Bernhard.
Topic: Left hand Precision (Bernhard Please Help)