My way of making decisions is to make lists! I look at them as dispassionately as I can and make the final decision based on the greatest need. So, in this particular case:
List everyone in order of immediate importance.
What are everyone's individual needs?
How well could they cope if those needs aren't met and what might be the lasting effects of that?
What are your own needs?
How will you cope if my needs aren't met and what might be the lasting effects on you?
Could you cope if there were a a negative knock-on situation?
Will the whole furore die down eventually, or is there a chance that a family feud might develop?
If I were facing this, I'd say it's a no-brainer - stay and help, at least for the 4 days requested.
Have an open-ended time frame to allow for possible complications (within reason - I'd re-assess things periodically and change my focus as the situation changes).
To me, the baby is the most important person, followed closely by its sibling.
Next, the children's mother (who has physical stresses as well as emotional), then their father (who hasn't).
My husband would probably come next, or even somewhat lower down the list if complications crop up!
I don't want to criticise someone I haven't even met but he sounds a little immature if he can't take a little bit of disruption on a temporary basis - not even for his own family. If he wanted the car, he should have taken it when he left and come back to pick you up when you were ready. You could try reminding him (gently) that he is not the centre of the universe! (On the other hand, you know what his reaction is likely to be to that, so only you can gauge his reaction to that piece of news.)
Sorry if I sound cold and calculating, but I do get somewhat wound up by people who act like spoilt children when there are other people (some of whom are children!) whose needs are greater.
Good luck, anyway, whatever you decide.
And congratulations to all concerned! 