OP, I have no experience or knowledge of USA, so can't comment on that.
However, I was also working part time when my FT dream job came up sooner than ideal i.e. my DC were 16 months, 5 and 7.
It involved a move of house, city and schools, but we did it.
Result? I love my job, we have money for a Nanny (who is absolutely brilliant and much better at messy play, baking, swimming, etc than I ever was), and a cleaner.
DC are happy, we are happy. I miss my friends from our old town more than the DC do because they have moved on and made new friends easier than I have.
However, I have flexibility. I can work in excess of 80 hours some weeks, including weekends, but only 40 others. I am senior enough that I can nip out for a class assembly (sometimes) and take the DC to school when one is ill. DH is also as involved in child care, household care as I am, so we are a partnership. I would be a bit more worried if you don't have some flexibility at work or your DH isn't able to partake in child/household care.
As you know, at the end of the day, only you can make the decision. However, if you turn the job down, there is no going back. If you accept it and it doesn't work, you can always quit.
Good luck with whichever decision you make.