This is an awful thread because it hits a little too close to home (just posted about a mouthy Lab). My instinct is to say put the dog down, but thus far I have not walked that walk myself (no broken skin with mine. yet.). The thing that throws me over the edge a bit, and I don't know anything about your situation with your DH, is that your DH would choose ANYTHING over the safety of his children and give you an ultimatum like that (choosing between him and the kids). Regardless of what happened prior, that in and of itself is reprehensible. DP and I are struggling with our dog, certainly, but if that came out of his mouth, I would show him the door, unhesitatingly and with extreme prejudice.
You choose your children EVERY TIME. EVERY TIME.