Weather was a pain for me as well. The best schedule I found that worked for an area with four seasons was to do Private pilot in Spring quarter (March-June); During summer, it was too hot during day so Instrument rating at night (June-Sept); weather is general good for Commercial in Fall quarter (Sept-Dec). Not terribly difficult to convince an Instructor to fly nights if its balls hot and he/she needs night hours. I found it much easier to access Class B/C airspace at night with a more relaxed ATC. Plus side, you will be able to get 100 night towards ATP mins.
Oh, don't get an aviation degree man! Plan worst case scenario. What if you lose your medical, or become un-insurable because of an accident or incident. Then there is always a chance of just getting hired and at the bottom of the seniority list but the industry tanked and you get laid off. You have a family and need to pay the bills. I bet a fall-back occupation with a non-aviation degree would come in handy
Besides, you will need a whole lot more than ATP min to get hired by the Majors.