I'd go with daycare because
(a) The cost should decrease over time as the kids get older, and you might be able to find a less expensive option at that point as well.
(b) You'll probably get occasional pay increases over time, so the financial stress will eventually lessen.
(c) It sounds like your current job is no good for your emotional state, which means it's no good for your kids and husband either.
(d) The daycare is only two half days a week, which doesn't amount to a lot of time in the grand scheme of things (in terms of kids away from you).
(e) You don't have to look at it as a permanent solution. If you take the promotion and really regret the decision, you can probably undo it (I imagine you could switch back to your old job either immediately or at some point).
However, I'd definitely discuss this with your mananger to see whether there is any possibility of slightly more money and/or a different schedule to allow you to choose a less expensive day care option or better afford the expensive one. Several years ago, my husband learned he'd need to work in another state for at least 6 weeks and possibly longer, and he was a big part of my child care and transportation to work. I was working 2 days in the office, the rest from home, and all full time. I had an almost-1-year-old, and I was feeling pretty stressed out. I reluctantly decided I'd need to quit if nothing changed, and I discussed the situation with my manager. I ended up being able to work part-time from home instead. Obviously, working from home isn't an option in your case, but my point is that if you don't ask for flexibility, you definitely won't get it.