IMHO the two issues are not really separate.

I think that one of the main issues you are dealing with is that your EX (or his wife is pushing the narrative).. thinks he is being taken advantage of.

I think that initially, he was willing to be generous, be the "bigger man" when his EX, the mother of his children, was dying.. and would before long leave him as the only parent.  He wasn't worried as much about a few rides here and there.. or even being flexible so you could have more time with the kids.. considering your diagnosis.

BUT.. now.. it's a few years down the road.. and either HE.. or his WIFE (she doesn't look all that sick to me honey).. is tired of being a nice guy (maybe not a natural thing for him.. hence he is your ex)... He has become less willing to be helpful and accomodating.. because.. "how long will he be expected to give up time.. and bend over backwards"

And.. when he asked for what HE/They thought was a reasonable pitch in for a used car, you declined.. because your finances aren't the same.. and you felt that he would be getting the relatively bigger benefit.  So.. maybe this is somewhat about saying "Hey.. you didn't think the car was going to help you.. I had to pay for it all myself.. I'm not going to let it benefit you".. and by benefit you.. it would mean relieving YOU of any rides.. giving you MORE time with any of your kids (when the girls want to stay over).

IT can also be about your girls getting ready to graduate and move on.. maybe he is feeling the fear of letting go.. and feels that he somehow gave up time with them.. thinking it wouldn't be for very long.. now they are getting ready to leave "home".

I don't know exactly what the best way forward it.. other than anything that you don't have to "ask for his cooperation or help).. is probably better.

I think that you probably need to stop asking him to provide rides on your week.  Either you, your husband need to take care of that somehow.. as difficult as that might be.  You need to stop being in the position of having to beg him for assistance. 

I also think you need to get the girls a car (have THEM pay for the car.).. and instead of paying your EX towards his insurance.. they go on yours with the car that you help them get.  I know it may not be super easy to swing that.. but I think they really need it.. they both are earning money.. and between three of you.. you will need to figure out how to get it done.

I'm not sure what you can do about your EX wanting to stick to CO days.. even when it is a pain for the kids and adults.. but clearly he has decided he no longer is willing to continue being the accomodating guy.

Whether he thinks you exagerated your condition.. whether it's just that he thought it would not be this long.. he is done being a nice guy about it.  you probably can't change that.. but you can change whether you have to rely on that jerk

^Agreed

Men think if you're not doubled over in a hospital bleeding out then "you're just fine" so get to work and take care of these kids. 
 

Ma'am you seem really sweet but unfortunately sometimes this world isnt sweet and these people WILL take advantage of you. 
 

You better start doing like this BM over here and tell him you can't do it (even if you can). And let him help you with those kids. Fake cry, put some ambiant hospital sounds in the background if you call him, run multiple guilt trips. Let your husband be your assistant and deal with him. I bet he will act right when he's dealing with another man. 
 

You're upset that he's not doing things your way. But he's not going to. That's probably one of the reasons you divorced. The two of you just don't have the same ideas, plans, and generally don't seem to get along. If you don't want to be at his whims, you have to get him out of it  He offered to go in on a car with the caveat that if you didn't, he wouldn't be letting it be used for your house or your benefit. And that's exactly what he's doing. Whether you agree or not, whether it makes sense or not, he's being true to what he said he would do.
 

if you can swing a car, which gives the girls the freedom and flexibility you're hoping for (on your weeks), that would be great. It allows them to help, it allows your husband to help, and it cuts your ex right out of the picture of needing to be helpful.

I also agree with ESMOD about timing. I know a lot of people when they divorce tend to give away the sun and the moon out of guilt, or out of the need to be free. When he heard you had cancer, he probably agreed to do a lot of things thinking it would be very short term. As you have managed to fight, he's turning back into an ex, and running out of helpfulness. Anything you can do to separate yourself from need to rely on him is better.

As for the CO, you won't likely agree there either. He wants the girls to cling to the CO until the time they grow up and leave the nest. You want them to come and go freely. I think this is a parallel parenting moment. You each raise them as you see fit. Don't encourage them to argue with their Dad. Leave their relationship in their hands.

If he's willing to continue driving your son, and you expect nothing from him in return, I see no harm in that continuing. But if it's like ripping off a bandage, and easier just to keep all transportation to the house it's in, I get that too!