PART TIME schedule

Hello! 

So to give you back story - I have been a NP with the same practice for 5.5 years. I started off (very poorly paid) as their first/only NP working 5 days a week, every other weekend and every holiday other than Christmas... I didn't negotiate well. 

Anyways, I proved my worth and slowly overtime things got better. In the past 5.5 years I had 2 paid maternity leaves (4 weeks and 8 weeks), 401k with some matching and better work hours. 

I am currently part time, I work a rotating schedule of tues or thur and then Friday and every other weekend. (SAT, SUN, TH, F, .....TUES, FRI, SAT SUN). I have asked for a consistent schedule (not rotating) for a while and with the kids starting schooling etc, its becoming difficult. I have also mentioned many times how as a part time employee I do not agree to every other weekend. 

I was told they'd hire another to help offload our workload (still trying to find the right fit), help with the schedule and the weekend rotation.

Am I asking too much for a set schedule (work every Tuesday and Friday ie.) and less weekend expectations (I.e. maybe every 3rd weekend)?