The only one who could answer whether you are going to be taken to Court or not is your mom, the potential plaintiff. What you should do is entirely up to you, and I don't say that because I'm trying to sidestep your question- family legal disputes are tricky and can be very messy.
Your mom could potentially sue you in small claims court. Disputes for under $7,500 generally go to small claims. The contract does not need to be signed by a notary to be enforceable, nor does it even need to be in writing.
If this does proceed to litigation, your mom will obviously say that the contract is the only (or at least controlling) agreement between the two of you.
You would have a few counterarguments available to you. Off-hand, (1) you could argue that the written contract isn't controlling, because both parties had the intent that it was not a real contract and would not be binding on either of you. (2) The car was previously gifted to you and became yours. At that point, your mother could not sell you property that was no longer hers to sell, making the contract invalid. (3) I don't know exactly what DMV slip you are referencing, but it sounds as though the DMV slip demonstrates that the car was already transferred to you and it was done so without requiring any more payments than had already been made. Given this, the new contract that you apparently signed could fail for lack of "consideration." For a contract to be enforceable, both sides would have to give something up. You already had an agreement for you to have the car- so what was it that your mother would have given up in the contract? If the contract didn't provide anything in addition to the car, you could make the argument that there was no consideration on her part, causing the contract to fail.
Additionally, there is a fraud possibility against your mother that may deter her from bringing any action. Who is this county worker and why did she need to demonstrate that she was receiving money for the car? Without knowing more, it sounds like there is a very real chance that there is some fraud.
However, with the legal issues aside, you may want to look into getting this all settled before it would ever get to arguments in front of a judge. This would be a very unfortunate situation if it causes ongoing friction within your family. It isn't that a car/$5,000.00 isn't substantial, but is it worth the potential damage to the family dynamics?