Prioritize. Don't worry so much about what your adult sims have to do aside from caring for the babies. Take care of them before they start crying. If your sim finishes breakfast, take a look at babies' needs before sending them off to do something else. Top everyone off with bottles and cuddles until they're good for awhile. The only thing you can't control is when the babies wet their diapers. If necessary, send your sims to bed a little early knowing they'll be getting up at least once during the night, so they'll get enough sleep before and after attending to the little ones. If you have two adults, keep one focused on the kids for a little while, allowing the other to attend to other things. When the caregiver's needs get low, send in the refreshed adult to take a turn at babysitting.
The store has that swing which I've heard is nice if you can afford it, but I personally don't have it. I also find the need-related lifetime rewards (meditative trance sleep, hardly hungry, steel bladder and dirt defiant) to be a big help in terms of reducing the time the adults need to spend on themselves.
