Being mad for this is both overaction and disrespectful to your gf.
Unless you are married or she is loaning your money or your car it's her business. Period. You're not "being disrespected" by her generosity to anyone else. Even if it's her ex.
If he steals her cash or wrecks her car the matter still wouldn't involve you.
The only time you would have cause is if she had decided to go with him to get his dad.
Have you asked her why she feels obligated to lend him money and her car? Has she ever mentioned why she allows this to happen?
Does this have anything to do with a debt she might owe him, or settlement amounts from their divorce (spousal support/alimony, child support, etc.)? If none of these apply to their situation; then it sounds like some boundaries are not being respected.
When two people are married they usually share financial burdens together. Once they become divorced, they are not responsible for each other... If this continues to bother you and you say nothing about it, you will begin to resent your GF and things will fall apart between you. You need to have an honest conversation about how this makes you feel and allow her to express her opinion about this.
Best of Luck
If they still have a good relationship, this is probably merely a reflection of that fact. She probably doesn't only hear from him when he wants something, they probably have an overall good relationship and you've just zeroed in on the money and the loan of the car.
I actually think it's kind of nice of her to loan him her car to go get his dad, as long as he's responsible about it and doesn't actually sponge off her.
Regarding the money, do they have kids together? They may be doing a whole lot of passing back and forth of responsibilities, kids and intertwined responsibilities, and if so, what is a little money in this? If he didn't repay it, as the poster above says, that is HER problem. If you are mad for her sake, perhaps she might think that is a little sweet but also very goofy (at best) and would think it is patronizing of you to judge her decisions with her own money. If you are mad because you think this somehow disses you, hey, forget it. It's not your money and your car, and in fact she's not your possession or even your wife, either.
This is her house too, meaning she has rights including the right to invite into it who she chooses. If you aren't married, you really don't have the moral high ground, and in any case even married women can have the father of their child come into their house and even into the kitchen or the loo. (Do you require all your adult friends who enter the house to ask permission to use the toilet? That seems rather odd.)
If you want more right to her consideration of your feelings, glowering and threatened-sounding though they seem, marry your girlfriend, don't just live with her. If you are not willing to make that commitment (or she is not), I'm sorry but you're on the same footing (when it comes to your roommate's guest requiring your permission to use your bathroom) as you would be with a roommate.
Especially since they have a child together, it is hardly surprising that she acts towards him in a comfortable, casual or more communal way. Do you think she is saying she wants him and does not want you? If that is not the case, then back off on the sulks and proprietary behavior. (If it is the case that you think she wants him and not you, talk about it with her.)
Regarding your above argument that she comes from a patriarchial place where the men pay the money to the women, so she should not be paying money to the man or his girlfriend should, please. Maybe she does not like living in a patriarchial place.
Is this the same girlfriend you posted about previously, who says cruel things to you like "go *** yourself?" Or is this a new girlfriend?