Sounds like your swaybar end link. Cheap and easy diy job 1/2 job.

You can check which motor mount it is. The top motor mount is the one on top of the motor. If the insert is cracked or torn then replace it. Cheap and and diy.
The right motor mount you can pull the pass wheel off and and peel back the wheel well cover. You can see the mount. There should be a rubber insert. If it broken or cracked. replace it. Not really a diy job.
Theres another mount and most expensive out of the 3. I dont think they wear out often. Its usually the other two. You should probably replace both at the same time especially since you have as much play in your engine. When the right mount is worn it tends to break the top mount as well.