You know you were BU to throw the wipes.
But like a few posters have said, it sounds like there is more going on here.
It may be he has some unrecognised SN. But that's not the first thing that sprung to my mind. I thought 'passive aggressive'. He does something, it's just wrong (not as in, not quite up to standard, but just totally wrong/not what you agreed together), result 1) you have to do the job yourself, so get no respite; result 2), when you discuss it with him, he plays the injured party 'but I tried! but I was making an effort! whatever I do, it's never enough!'; result 3) you can never relax when he has responsibility for something; result 4) eventually you reach your limits and react more strongly than you yourself think is ok, e.g. throwing things; result 5) it messes with your head, you feel guilty for everything (from not appreciating his efforts, to blowing up).
The other thing that sprung to mind is, this is just THE classical way of getting out of doing stuff. For some reason he thinks it is more ok for you to do these things, than for him to do them. And actually he's got you right there now, where you are considering doing them all yourself and letting him off the hook, as it is less trouble. Is he capable in things he cares about? Well then if he is incapable when it comes to household/childcare things, I suppose it means he doesn't care about these things. About you and the children. Perhaps tell him that this is the message you are receiving?
Has it occurred to you that he is actually actively sabotaging your work for your degree? Does your studying bother him?
All that said, I still agree with those who say that if you want him to take responsibility for certain things, you have to LET him have the responsibility. He needs to do it his way, and unless it puts anyone in danger, you need to accept his way as ok.
FWIW, every time it is DPs turn to pick DS up from nursery school, he asks me at what time he needs to be there. At one point I turned around and said, 'if I wasn't here to ask, nor at the end of a phone line, what would you do? Would you end up picking him up late?' He said he would check online. Yes, asking me if I'm in the same room, is easier and quicker, but if I wasn't there, he would very quickly learn to turn on his brain and would simply remember, rather than have to ask OR look it up!