We also do what Kara calls quiet time. At first it was hard and nobody wanted to do it, but now everyone looks forward to picking out a few toys and playing alone with them. It is a great time for parents, too. If you are able you could get a few toys or puzzles especially for the occasion to help it go smoother.
I would suggest you make a list of all the things your kids like to do and/or you want them to do (i.e. play dough, drawing, legos, games or puzzles, paper dolls, reading, tv, etc.) then divide the day into 30 min. segments, including "family time" and alone time. If you are dealing with sibling rivalry, a good way to deal with that is having the child/ren causing problems sit out until that activity time set is over.
Good luck working to have a smoother holiday season and maybe making some ongoing scheduling for weekends. Kids really do thrive on some sort of routine or planned out days.