Sam's Family Spa in Desert Hot Springs. Family friendly, great pool, great mineral pools, plus a sauna
Close to Joshua Tree for some great hikes. Take the back road for some fun up and down road sections in the TV!
Palm Springs/Desert Hot Springs is a long trip from Santa Cruz, we've made the trip many times. Call now if you want reservations after Christmas, it's very popular and there are tons of people from up north going there at that time of the year.
Sam's also has hotel rooms (not fancy) with kitchens that might accommodate you. It's less crowded after New Year's, depending on what day of the year it is. Our kids loved Sam's. We haven't been there for a while, but they had a clubhouse with ping pong tables, a pool table, & TV. It's not new and sophisticated, but kind of funky and comfortable (and clean).
Sam's is a little bit away from Palm Springs, but there are stores, restaurants and other services within a short drive. The Coachella Valley Natural Area is pretty cool too.