Management is trying to force me to work Fridays

Hi! Wondering if anyone has dealt with this. Backstory, I work in a rural hospital and our RT department does a lot of outpatient to make up for the fact that our inpatient volume is often low. We live in a very expensive area, and are consistently staffed by travelers to fill in the gaps. We have 1 part time, 1 PRN, and 2 full time staff RTs. The full time RTs rotate weekends and shifts during the week, except for Fridays because neither of us have childcare on that day. In the past, we have used a traveler on Fridays and any other day of the week we need help. We typically work 2 RTs during the week and 1 RT on weekends because we don’t do outpatients on Saturday and Sunday. Our dilemma is that we are now being told by upper management that they are no longer going to cover a traveling position. Meaning Fridays are going to need covered. My issue, and I think my coworker agrees, is that I already work every other weekend. I’d have a different schedule if I could, but childcare is expensive and working 2 week days and every other weekend is a cheaper option. Now I’m being told that I’m going to have to “figure something out” for childcare on Fridays so I can work. I told them I’d work more Fridays but I’m not going to work every other weekend anymore. If I’m going to have to procure more weekday coverage, then I shouldn’t have to work every other weekend. Being asked to work Fridays is also taking that little time I get with my son, who goes to school Monday-Thursday. TLDR; I’m being asked to work a day that I don’t have childcare available, and have basically been told that I don’t have an option and that I need to figure it out. Has anyone else been in a situation where they’re basically being forced to work a day where they don’t have childcare? What did you do?