When you become a stay at home dad, there are adjustments both you and your spouse have to make. If you've fallen into the stay-at-home gig, like I did, instead of truly choosing it, I suspect the adjustment will take longer and have a few bumps in it. Mine certainly did.
Much of course depends on your spouse and how the two of you shared house duties before. I'm assuming here that said spouse has some sort of standard career, by the way.
At first, we did things where she got our son ready for school three days a week, and I did it two. It was her idea, and it seemed to make sense at the time, since she was getting up very early anyway in order to pull herself together and get to work on time (my wife is not a morning person. Neither is our son, and I managed by having a sort of ritual that got me through the first hour or two, but woe betide anyone who messed with my ritual). This arrangement lasted maybe two weeks.
Trish came to me one day and stated she couldn't do it anymore, and that in fact she was feeling jealous and even angry that I was getting to sleep in so much.
And here I think I should take a second to make a very important point: In my case, having left a job that was beginning to suck the life out of me via benign neglect, any change for me was one for the better. I loved what had happened to me, and why should I want to change what was fun and nice? Let it be known that had circumstances been reversed, it would have been me standing there demanding, not asking, that we do things differently.
And so we changed it around, from two days to three days, and eventually to one day. And it made sense. Okay, Trish was getting up early anyway, but she was trying to get out of the house and go to her job. I was doing my bit around the house, but I didn't have a hour-long commute.
And that is something you have to recognize and get used to. Your spouse may have done a lot of the traditional "Mom" things like getting the kids ready for school while getting herself ready for work, but if you're the one going to be at home, and you aren't having to get ready for work, then you're the one that needs to take on someone else's responsibilities to make things work.