We've hsed, done ps, and done partial hs/partial ps. Right now, my kids are in school more than they are home but I am trying to get my ducks in order to bring dd#2 back home due to social concerns as well as really feeling the math is not working for her at school.
If you are working opposing shifts with you spouse, this could certainly work with your both working but you need to be aware that you are basically taking on two full-time jobs. You will be at work for whatever hours you are there and then coming home to do your second job as a teacher. I have one friend who has made this work, but it did wind up for some time with her dc kind of teaching himself b/c mom had other obligations when she got home -- cooking dinner, house stuff, etc. -- all those things that we all need to do when we are not at work.
I, too, had thought about a co-op where the parents could trade off who is teaching the kids from day to day/hour to hour such that parents could at least work pt. I just haven't been able to find enough local parents who were willing to commit to that to make it viable for us. One of my friends who hsed completely for many years said that her co-ops always fell apart b/c she felt like there were a lot of unstructured unschoolers locally who just didn't seem to fit well into keeping a scheduled program like that work. The co-op idea is very appealing but will probably depend on your local population of hsers and your contacts within that community as to whether you can make it work.
You could, of course, pay someone to take your kids while you are at work and do the hsing for you. The question then becomes whether that is financially viable and if it makes more sense to consider a private school at that point or if hsing is still the better option.
We do have a number of local hs supplements such as Options
and some religious based ones where hsed kids can go for a day or two a week. That would provide some supplemental time where you could work if you can find something like that.