No, I do not think you are wrong on this. No one should be treated with such disrespect. It does not sound like you were overreacting at all. But, there are a couple things that aren't clear in your post. First, you don't mention what reason he gave you for having you pick up the baby instead of him. Did he say it was because he was tired and needed a nap? Was it because he had to work late? Or did you not even ask why he wanted you to pick up the baby? The answer to this question could help understand what exactly happened yesterday. Second, you mentioned that your husband had stopped contributing "lately". Have you had any type of discussion with him about these changes, besides what happened yesterday, or have you just been ignoring it, hoping he would get out of his "funk" on his own and go back to the usual schedule?
The only way you're going to know what's going on with your husband is if he tells you. If his first reaction is to blow up at you, I would let things cool down and then approach the subject again to see if you can find out what's up when he's being rational. If he still doesn't want to talk, or reacts the same way, you probably have a problem on your hands that will take more time or some outside help to get through.
The short answer here is it's obvious there's something up with your husband and there are a multitude of reasons why this is happening. You need to find out what that is before you can try to help him get past it, if it can be helped at all. I agree with the other mom who said trust your instincts. Don't jump to conclusions, necessarily, but make sure your words and actions are helpful in finding out what's going on, rather than contributing the problem, in case it's simply stress, depression, or some other issue that your home life is causing.
Your schedule does sound hectic, but it sounds like you guys had a good balance of chores before he stopped helping. When my husband all of sudden doesn't want to do his part, it just doesn't get done. I'm not going to all of a sudden take over his chores as well as mine without a good reason. Marriage is a partnership, and even the way chores are split in a marriage can have legally binding implications in the case of a divorce.
Try to find out what is going on and then react accordingly. There's no use trying to guess why this is happening. I've been married 16 years and I still can't tell why my husband does some of the things he does. :-)
Good luck!
Blessings,
N.