Help a family find reliable winter transportation

I know this is asking a lot, but anything helps, even $1 or a repost! :)

(After trying multiple used car dealerships and Facebook marketplace I haven’t had any luck.)

I’m not one to ask for help, so this is quite embarrassing for me, but here I am now, asking everyone for help to get my first car and/or to repair my mom’s car so we have a safe and reliable vehicle for the winter when it snows. I finally got my driver's license after having such a fear of driving, and now I’m trying to save up to get a safe and reliable vehicle. Getting my first car before winter hits will make life easier in so many different ways and help my family in general. I’ve been driving my mom’s car lately, but it has a lot of issues, and I’m worried it won’t be reliable enough to drive with my son in the vehicle when it snows, as it has issues with the heater, not starting, and the tires. (If I still don’t have enough for a down payment for a vehicle of my own, I will put this money towards fixing my mom’s car for the winter.) As many of you know, the price of living is extremely expensive, especially as a single mom. I recently had to move with only the clothes on mine and my son’s backs due to an abusive relationship. I’ve been working hard to replace everything we had to leave behind, but I can’t seem to work hard enough for a good down payment for an all-wheel/four-wheel drive vehicle that I will feel safe enough driving from point A to B with my son in the vehicle during the gnarly winters here.