Hello KelliTravels :)
I've been traveling for 2.5 years and haven't requested specific days off within a contract. Most places that I have been to has worked with me on getting days off or getting a long weekend. Most of the time I ask another co-worker to trade for me and has worked out, I try not to reduce my hours. I've never had a problem doing it that way. At times it can be an event, I worked every Thurs-Sun in NM and it was like pulling teeth to get a Fri-Say off. I was there for 7 months and only got one weekend off. If your not in a contract you may want to request those days off, I've had another traveler working with me that requested a holiday off and got it before they started the contract.
I often get stuck with working the last days of my contract, most of the time my contract ends on a Friday and I move out on Monday or Tuesday depending on where I'm going next. I had one assignment in TX that ended on Friday and had to be in NM to start on Sunday. Whew, that was an all day Saturday driving in the middle of nowhere in which I ran into having a dead battery in my car which made the trip even longer. And worked 8 days in a row clearing 90 hours for the week. Talk about needing to recharge after that. But I choose to be busy at that time, another time I was off a month (not my choice). I guess we take the good and bad of travel life. LOL
I would talk with your company, most of the time if it's a few days that can be swicthed around at most hospitals. Good Luck and Happy 5th Anniversary :)