Thanks for posting. It is a tough question, esp with 2 kids. An MBA will take you out for a few years and put quite a lot of strain in terms of work load. Neither option is ideal as both are risky investments.
Carey is not even ranked by US News. It is a new program, and their Flex MBA is even newer than that. It is worth reading some reviews though:
https://gmatclub.com/reviews/business_school/carey-94 - they seem to be generally positive. Since you are doing a Healthcare MBA, I think John Hopkins would make more sense since they are so well known for the med research school. I think it would be an easy intro/foot in the door in a few cases.
As to Weatherhead, even less is known about that program.
Since I see a lack of info for Weatherhead, I would suggest either Carey or re-evaluating your opportunities in more established places such as UNC or Fuqua next year. Your dollars would go a long way further there, though I can imagine how tough it is to apply, study for the GMAT, and all else with work and 2 kids.
It really depends on why you need an MBA. if you need one to get a promotion at your job and your employer is paying for some of it, that's great, and in that case go with an easier option. If you are going to have to recruit and look for a job on your own, then you need to see which program provides more support for getting a job and employers lined up or has more supportive Alum base in places you are looking to work at.
Good Luck!