2001 Toyota Corolla CLUNKING SOUND WHEN DRIVING

Hi and thank you for your help.
I'm very frustrated. The car makes a severe clunking sound when driving. If you accelerate, and then leave the accelerator, the car goes KLUNK loudly. The tranny is ok - no slippage. The engine runs fine. 2 engine mounts have been replaced already but this hasn't fixed the problem. It seems that the rear engine mount could be bad, according to one mechanic. Another mechanic says, that the tie rods are bad since the passenger side wheel has play and makes a loud knocking sound when jostled on the bay. The tie rod argument makes sense, but could it be that the rear engine mount is also bad?

I am not keen to put much money into the car and am wondering what to do. Please advise at the earliest.