Yes, this is a most common problem. It is also the reason why hands together is 37 times more difficult than hands separate.
What you are experiencing is called
sympathetic movement. There is really no reason why the hands should move in sympathy, but they do. So what you need to do is to learn how to inhibit sympathetic movement. This is done at the level where messages get sent from the brain via the nerves to the muscles (the nervous level). Typically people try to inhibit sympathetic movement (mostly unconsciously) at the muscle level, that is, by tensing the muscles. People who do so typically experience a “freezing” of motions. So remember, this has nothing to do with muscles, but with nerves.
To learn the skill it is no good to start with improvisation straight away. This makes it too complex. Start with something written down (later you will be able to transfer the skill to improvisation.
Now start with the left hand. Repeat the rhythmic pattern/chord progression (which can be as simple or as complicated as you wish – but always better to start simple), until it becomes so ingrained that you can do it
automatically, that is your left hand goes through the motions and hit the correct notes without you having to think about it.
Now you are going to play one single note on the right hand, and keep going with the left . Even this single note may throw the span in the works and the left hand will fall apart. Never mind, just try again. Your aim is to be able to “drop” so to speak, the single right hand note, without it interfering in any way with the left hand
movement pattern (yes, this is all about movement patterns). You may even make mistakes in the right hand, but you are not allowed to make any mistakes on the left. Then proceed to no mistakes on the right. I cannot tell you more than this. Just keep repeating until you acquire the knack to play a single note with the right hand without in anyway interfering with the (more or less) complex left hand rhythm/movement pattern. Once you can do that, add a second note. On the right hand. Now you are playing two notes on the right hand. Again it will all fall apart. Don’t lose heart, keep working at it, and soon you will be able to do it, in fact quicker than with the first note, because your body will have learned what is it that needs to be done. Then add a 3rd note and so on.
As you can imagine it is better to work in small passages to start with.
One last thing. Once you can do your passage perfectly with both hands, repeat the whole procedure, but this time dropping the left hand notes.
I call this “dropping notes”, and you can find more information about it here:
https://pianoforum.net/smf/index.php/topic,1651.msg14344.html#msg14344(How to gain hand independence – dropping notes)
https://pianoforum.net/smf/index.php/topic,2173.msg18976.html#msg18976(dropping notes by comparing it with patting head/rubbing tummy)
https://pianoforum.net/smf/index.php/topic,3085.msg27140.html#msg27140(Hands together: when and how – dropping notes)
https://pianoforum.net/smf/index.php/topic,3085.msg44855.html#msg44855(Hands together – dropping notes – when to learn HT and when to learn HS)
You may also find the following thread interesting although it is not quite applicable to your particular problem:
https://www.pianoforum.net/smf/index.php/topic,7682.msg77042.html#msg77042(hand independence: how to create a cue system and what is hand memory).
Best wishes,
Bernhard.