A City Vehicle Hit My Car, Can I Keep The Money?

Location: Texas, USA

Back in February my vehicle was hit by a city vehicle while it was parked in front of my house. It was a whole situation of the the city vehicle pulling in front of mine and they got out of it and forgot to put it in park and it rolled back and hit my car, damaging the front. I witnessed the whole thing happen in real time. We went through all the hoops and finally got the issue settled. While talking to the rep for my city they continuously tried to give me the smallest amount for my car and tried to tell me it was not worth that and we fought over it until I proved what my car was worth. I gave them the estimate from the body shop I had gone to but my husband wasn’t sure if we’d go there for sure. I asked the check be made out to me personally so I could chose the shop and get the process moving. They said it couldn’t be made out to me and would have to be made out to the body shop doing the repairs. The only way the check would be made out to my name was if I did the repairs myself and gave them my own estimate and then did the repairs, only after I gave them receipts and proved I repaired the car would they give me a check written to me (basically reimbursement). If I didn’t want to make repairs then they give me the smallest amount of money and leave it.
Here’s where I’m confused. I finally received the check in the mail and when I opened it, it had the repair amount but the check was made out to me personally and not the body shop. My husband and I were going to get rid of the car after the accident and just use the money towards a new car since it’s very old. We were only going to fix it since we had to and so we could sell it for more than the city was willing to give us.
I have combed through all the emails and the one paper they gave me to sign and it doesn’t say I have to prove that the repairs were done by the shop or anything like that after I receive the check. Since I assume they accidentally made the check out to my name instead of the body shops and we were only fixing the car because we “had” to, can I keep the money the city sent me and just put it in my bank or do I have to repair the car?