Two separate issues maybe?

Tamra, improper battery ground can cause lots of problems. you should never be able to wiggle a battery connection. it should be removed, cleaned and tightened. if it wont tighten, then it needs to be replaced. same with the positive end. Also, when this issue is fixed, charge your battery fully, and have it load tested. it might be bad.

I'm confused though because it doesn't seem to be the ground at all or appears to be the wire itself?

But that also shouldn't make the engine shake??

Fix the battery cables first, get a good battery in there and fully charged, then see if any other problems exist. Your car may have been losing electrical power when it was running causing a host of issues. An engine shaking is from misfiring which may have been due to your bad battery/wiring. Remember you have an engine computer that requires electricity to work.

Battery cable connections need to be absolutely clean, free from corrosion and tight. If the negative connection is clean and tight and wiggling the wire causes it to start then either the battery, battery cable or the cable's connection is the problem. Fix the battery / cable issue first and proceed from there to the next issue.

Agree. This all sounds like an electrical issue. Make sure all connections are clean and tight. Replace battery if it is weak or more than 5 years old. Unrelated, but important to check while you're at it are the spark plugs. They last so long on modern cars that they sometimes get forgotten altogether. Might be time for new ones. They will also cause misfiring issues if they are bad enough, although in this case I think the misfire is from the electrical issues mentioned above.