The big thing to understand is that while it's attainable, it probably won't be attainable right away. Everything is based upon your seniority at a company. While on reserve it's realistically probably not going to happen until you are senior on reserve. Then once you become a line holder you'll now be one of the junior line holders... So that might make it tougher to hold 5 off in a row. The plus side to being a line holder though is that you tend to get more days off in total than as a reserve pilot. Once you obtain more seniority it gets easier. To that, you might want to look at regionals that are experiencing a lot of growth so you climb the seniority ladder faster. You might also have to accept that in the beginning, you might not be able to pull your weight as a care taker, the trade off is that down the line you can take a more active roll. Someone mentioned looking into FMLA, so that might be a good avenue.

Otherwise there are 135/fractional operators out there that work on a 7on/7off schedule. The entry barriers might be higher than getting into a regional at the better paying places, but the schedule would align with your responsibilities. Wheels Up comes to mind, I think Planesense has a 7/7 schedule (not sure).