This is a tricky one; I was in a similar spot recently. My sister and family, who are a bit precarious financially, were embarking on a move out of the city to a suburban area with very few non-car options. I was considering replacing my 2002 Civic, as it was coming up on 300K, even though it had lots of life yet. I realized that I was in a position where I *could* gift it to her.
In the end, I did, and it made a massive difference to their family that I feel really good about. Although the car wasn't worth much in cash, it has been priceless for them. On the other hand, I did get cranky about having to spend new money on a replacement sort of unnecessarily. If they hadn't been in the picture, I would likely have driven my old car for a couple more years trouble free, and financially that would have been nice.
Family is important, imho, and I have no regrets about sacrificing a little financially because I could do so responsibly. If that sounds like the right thing to do in your position, go for it.
I know sometimes it's hard to quiet that voice that says "all spending that's not on NEEDS is hedonistic lifestyle inflation for fools!!" But truthfully, you're not talking about a lot of money for something that sounds like a win-win for everyone involved. If you're going to spend $2500 on a new car, that money's better off staying in the family anyway, right? :)