just my thought I think maybe you could do friday and if possible maybe saturday morning that might give you more time for everything else I am not sure if saturday mornings work for you but that would give you enough time thru out the week to get everything else done or even if there are saturday hours are available at the job offered
I think you have to do what your intuition tells you will work out best for you and your family.
My outside observation is that it seems perfectly do-able, and would enhance the time you spend with your family by reducing money concerns.
Well, my first thought is to turn it down. If it's not a good fit it's worth it to find the money elsewhere in the budget, or perhaps pick up more cleaning jobs, or to just carry on. But then thinking more carefully....
I don't think that for now you have much to worry about for homeschooling. You don't have to homeschool exactly Monday through Friday, so if you have one week day off and homeschool on the weekend that's ok. And you don't have to even homeschool in the daytime either. And since it's kindergarten, it's especially ok. There's a lesser volume of schoolwork involved in kindergarten than in the upper grades (I'm not bashing Kinder, I was a kinder teacher, just that there's not as MUCH of it as when they get older.) So you have a lot of flexibility there. Dh can do it just as well as you if you lay it out for him, even if he hadn't planned on doing it. He'll figure it out eventually.
I went back to work this winter and even though my dh was a -didn't-have-to-do-anything-except-go-to-work kind of guy, he surprised me by rising, somewhat, to the challenge. He did suddenly NOTICE that things just didn't get done without me doing them and so he started noticing things and getting it done.
As for housework, I think men do better when they are put in charge of a few things, but then they alone are responsible for it rather then when we say, "And can you do this today, and that tomorrow." Could he do all the laundry each week? Or would he rather do the dishes EVERY night without being asked? Have him decide which things he is taking on and then back off and let him do them his way as long as it gets done.
You can always readjust later as his work schedule changes. If you need to quit, you can give plenty of notice and offer to train the new person before you go so you don't cause hard feelings.
I'd probably take it.
I would go for it.