Keep it simple and just have them pay 52 weeks. Don't try and do a different number of unpaid days off for each family. What would you do for the 3 day a week family that switches part way through to 5 days? Would they get 5 days that year? Too complicated long term.

Depending on what your area (or clientele) will support either just get paid for your days off, get paid for vacation but not sick days, or some paid the rest unpaid.