my DD is like that, too. she will be 4 in april. i have a DS who was born in Sept. so i have gone through it, and am still going through it.
we did enroll her in gymnastics. that's on Wednesdays. Preschool is Tues. and Thurs. (2.5 hours in the morning). i also signed her up for story time at the library (Mondays), and there are occasional special programs on Fridays.
it takes A LOT to wear her out.
sometimes, by the end of the week, she is tired enough to fall asleep easily by 7 pm. i don't bother trying to get her to nap. she resists it strongly. and when she does nap, it totally ruins her bedtime later in the day.
might i add that i am 41, so not a *young* mom, and, to reiterate, this girl is seriously active. some might say hyper. i have thought hyper for awhile now.
one thing she will do, however, is play by herself. i am able to go back to bed with the baby, put the TV on PBS for her, and when i check on her, she has gotten out her stuffed toys or dolls and set up elaborate imaginative play with them, using whatever props are around. i don't think she usually sits and watches the TV, more like she gets ideas from her shows, and "acts" them out with her toys. and she is able to entertain herself like this for a couple hours while i get a bit more rest.
a couple other suggestions for wearing her out: go somewhere. i don't know if you can ever make a trip on the train or by car, but i find that the stimulation of being gone all day and in new environments, wears her out pretty good!
also as others have suggested, playdates are great for wearing her out.
does your baby sleep well through the "noise" of the older child? if so, lucky you. mine didn't. he's starting to settle down and we're in a better groove, now that he's 5 months old. but he sleeps only for about a 1/2 hour at a time, but does so every couple hours throughout the day.
oh, one more idea that works for us. i put DD in charge of DS's entertainment. she is *GREAT* for this. i tell her how much he looks up to her, and wants to be just like her, she totally eats it up. she lets him pull her hair, they "talk" to each other, she's showing him how to crawl, she'll practice rolling over with him, etc., etc. in MANY ways it is easier for me as a parent to DS, to have DD around with me. when i need to use the bathroom, i'll put him on his tummy time mat, and ask her to talk with him, or show him a stuffed animal, and she really helps a lot.
it will get easier as your new LO grows and is less "fragile". i keep telling DD that by summer DS is going to be her little playmate. i do believe that that is when it will really get "easier". he is going to be the kind of brother who plays dolls and dress up (he will have no choice with the firecracker of a sister he's got) and he'd better learn to talk if he hopes to get a word in edgewise on her or speak for himself!!
oh well, thanks for listening to my story. glad to know i'm not the only one with a seriously active preschool daughter and a baby!!
ps: i have every confidence that a girl like we've got is going to grow into a driven and accomplished woman some day.