I had two kids during my PhD program, my spouse was a stay-at-home parent during this time.
I would strongly recommend looking at what support your target graduate schools have for parents/new parents. This varies greatly between schools. I went to Princeton for grad school, which provided 12 weeks leave for a new primary parent (new mother, primary caregiver of newly adopted kid) and an additional semester of funding for the primary parent, among other things. They've expanded financial support for students with children since I was there, and it's even better now.
I'm not saying this to say that Princeton should be a school you should choose (there are lots of factors going into that), but just providing an example of what at least one school does provide. (And I acknowledge that Princeton has more financial resources than many schools to be able to provide these things.)
And also, even though the school provided this support and required an advisor to be okay with it, that didn't mean that every advisor on campus would've been okay with it. I didn't hear any stories to this end (which is a good thing), but I imagine some advisors may be resentful to have a student take 12 weeks off even if the university is financially supporting them during that time.
With my spouse staying at home, we never had to look really hard at childcare options. But from what we have seen and heard, on-campus childcare options that would've been available to us skew towards the higher end of costs of all available childcare, on and off campus. But where we were at, public transportation options were limited, so those who used off-campus child care and didn't have cars spent a lot of time transporting everyone even for relatively nearby places.
Cost of living should be a major consideration. Having children means that your housing, food, and transportation costs will be more than your child-free counterparts, and locations with higher costs of living will only compound that effect. Living in New Jersey was expensive and so our housing options were extremely limited (we had to live in low-quality and small on-campus housing), while if we had gone to some other schools we probably could've rented a much larger place, maybe even a single-family house. There were reasons we made the choice we did, but different choices would've had different advantages financial-wise.
By the best study we could put together, we estimated about 4% of grad students at my university had children. There are disadvantages that come with that. We would have friends get Child Protective Services called on them by student neighbors for just normal kid crying, and a lot of students were more annoyed by the presence of children on campus and in housing than anything else. Other universities will have larger fractions of grad students with children, and I imagine will have fewer of these problems.
And in the end, I would advise at least one of you to visit the university and department(s) you'll be at. My wife was pregnant at the time that I was invited to visit departments who had accepted me, and I asked lots of questions about family support at such. The department I ultimately chose had lots of positive things to say and show about being okay with grad students having kids, and that played out in practice. My advisor was supportive of my having children, they would come visit me in my office regularly and it was never awkward, and they were always welcome at department parties and other functions. I know not all departments on campus were like this.
In the end, I'm glad I didn't wait to have children until after grad school, but having them in grad school was much more difficult than I imagined it would be. Having both parents pursue PhDs simultaneously adds a whole other dimension of difficulty and complexity that I can't even imagine what that will be like.
My undergrad research advisor had kids after he finished his PhD. When I told him that we would be having a kid my first year of graduate school, he told me that he wishes he would've started having kids in graduate school. That's his experience, I can't say that that would be everybody's experience, and I don't think he and his spouse were pursuing simultaneous PhDs (they both do have PhDs).
In end, having kids in graduate school definitely decreased the quality of my research output. I performed well enough to graduate without problem, but I had trouble managing my time and mental energies in a way to be completely successful as both a parent and a developing scientist. But I don't regret that sacrifice to have my kids when I did. But it was a sacrifice to the quality of my PhD for me. And in the end, I took a different career path post-grad-school than I imagined pre-grad-school so that I could have a better work/life balance. I "left the field" as my academic colleagues would say, and in that sense having kids in grad school took me completely away from the academics of it all. But I don't (usually) regret that either.
From my experience only pursuing one PhD while having kids, I don't see how pursuing two PhDs while having kids is practicable, unless one of you is willing to be the "primary caregiver" and give much more sacrifice than the other as far as the quality of their PhD education, or you both end up with extremely understanding advisors and programs. And even with that, it's likely that your PhDs may take significantly longer than they would otherwise.
From the kids' perspective, they think those years in the dinky apartment with a busy dad were great, they don't look back on those years with any bad memories. They loved where we lived and the friends we had there, and they were so young the "bad" aspects, at least to me, didn't affect them very much.
