I agree with the rest of you guys that wheel balancing could cause a vibration but the vibration would be constant, not just on acceleration.
The fact that the car only does it when accelerating tells me that the engine is hesitating under load, probably due to bad spark plugs or weak coils.
This is just my opinion though, judging from what I’ve read. I may or may not be wrong. I can’t properly diagnose a car that isn’t with me, I can just make educated guesses on the information supplied.
You have already replace the engine and transmission mounts so that’s ruled out. The person that told you to do that isn’t a professional mechanic. Professionals fix the problem first time, not guess and swap parts at the customers expense and hope the problem goes away.
You need to find a proper technician in a proper garage. All any of us can do here is offer educated guesses.