Re: daycare providers -- how do you do it?
You're a saint. Time with a wee one inherently does take time from the older kids, & while I'd do a lot for family, I don't know that I'd add a fourth to my daily schedule with no compensation. And 10 hr days are loooong days.
That said, I think some of the suggestions are great. A cohesive schedule is a great place to start; I know that 3 month olds can't really be "scheuled" yet, but it lets your kids know what to expect & the loose structure may make things feel more manageable for you. Two good naps for the baby...gives you some time with your kids. If your kids also have some free-play or down time, separate from baby's nap time, you could put baby in a bouncer, swing, etc., to try to get some things done. I just know that, outside of the bouncer, DD's needs seemed incessant at that age. It was just a rapid cycle of feeding, burping, diaper changing, putting down for sleep, doing a couple quick things, picking up from sleep, rinse, repeat.