I fall into category (b): male who was a single parent, and primary carer, during grad-school. In my particular case my PhD was a research degree (no coursework) in statistics, and so I did the vast majority of my study and research from home. During the day I would look after the kids, and sneak in some research time when able, but most of the research was done after their bed-time, or at free time on the weekend. I also found that I was constantly "mulling" over my research and ideas when I was looking after the kids, so there was also a certain amount of subconscious work going on at those times. I had the luxury of being in a program that could almost fully be done from home, since it had no coursework, and involved research in mathematical things that can be done mostly on paper and a computer. Consequently, my experience is probably substantially different to someone in a program that requires course-work or laboratory research. Nevertheless, I will give my experiences for whatever they're worth.
Although I did most of my work from home, I had a monthly supervisory meeting plus time on the university computers to download a new set of papers for my research. There were also sporadic occasions where I required attendance for some administrative matter, or some aspect of research where I needed new materials that I could only get through the university. Naturally, attendance at the university was a big chore, since I had to get the kids ready, bring a lot of paraphernalia, and I also had quite a long bus ride each way. For supervisor meetings I would take the kids in with me, and they would do some colouring-in, draw pictures on the white-boards, and other activities. This was usually enough to occupy them for a short meeting, and my supervisors were nice about it. I made use of occasional baby-sitting from family members, but I mostly relied on homework. One thing that I found worked well was to make an effort to ensure that trips to the university were a fun activity for the kids, so that they would be in good spirits. This meant having a routine where we would always go and get a treat after my supervisory meeting. That meant that they had something to look forward to and I also had something to "bribe" them with to stay on their best behaviour!
I found that dealing with grad-school was largely a matter of organising my research agenda in a way that required as few attendances as possible, which meant that on each visit I needed to give myself enough material to do over a month. The experience of full-time study plus raising children kept me busy, but it was less hectic than if I had been trying to work a full-time job plus instead of doing grad-school. I found that this was one of the major advantages of grad-school over full-time work; the additional flexibility in attendance and time usage made it easier to spend time raising the kids. In that respect it was perfect timing; it meant I didn't have to use child-care facilities and I could give my kids a fun childhood at home with a parent.
While I wouldn't presume to know your circumstances well enough to tell you what to do, one aspect of your post that strikes me as helpful is the fact that you and your husband are both in grad-school at the same time. An option in that case would be to live on campus, or close by, and "juggle" the kids between you to minimise the need for outside care (e.g., one goes to class, the other cares for the kids, then swap). Obviously this depends on the constraints of your program, so maybe it is infeasible, but it is worth considering how well this could be done.
