I have three kids, ages 9, 7 & 4. We have run into a bit of a snag with Piper, and so I'm coming to the experts!
If Piper nips or mouths my husband or myself, we let out a yelp. This has been quite effective. The kids, however, can not master the yelp. They will say OW! or scream, but we can't seem to get them to mimick the yelp. And Piper has decided they are playmates and she is constantly biting at them and jumping on them. An adult is always present and we correct Piper by saying OFF or NO BITE and giving her a toy to play with. She very quickly escalates from play to growling and nipping after several corrections and we end up crating her for time out. She's also taken to jumping up and grabbing the crotch of my sons pants. Definitely not ok.
The kids do not play rough with her or encourage chasing, etc. This typically happens the second they sit on the floor with her.
She gets lots of exercise playing with our outside dog and running and chasing toys. She is, for the most part, pretty mellow. As I type this, she's snuggled on my lap looking quite innocent.
Of course, she has NO idea what "off" or "no bite" mean at this point, so although she might make the connection eventually, right now, you can't expect that to help much.
Other than that, is sounds like you are ding the right things... getting the kids to play with her quietly on the floor, and if she ramps up to an unacceptable level, isolating her. (for short periods) Keep working with the kids on both their "yelp technique"<g> and also "be a tree", where, if she jumps at them they just stand up, turn their faces away, and don't move a muscle. This is a form or isolating or ignoring too... where hopefully, after a while, she'll get the message that fun ends when she gets too rough.
Another thing that might help with the older two, although your 4 year old is probably too young, is to get them involved in her training. Take them to Puppy K with you, and let THEM work with the trainer on how to handle her best. At home, try to structure their "play" time so that it is actually training time for Piper. Teach them to practice her sits and downs, making sure they dole out plenty of small treats for doing it right. Another GREAT "training game" that is a precursor to formal recalls is to have one kid sit on each end of the longest hallway you have. (your 4 year old can do this one too) Have the children, one at a time, call her back and forth, delivering a treat, praise and soft pats when she arrives. Then the other child calls her back the other way. This can burn off a LOT of excess energy in a positive way.
Most of what is going on is just plain puppyhood and most, if not all, of it will wane naturally with your consistent good work over the next few months. If it feels like it's becoming a problem you can't handle, I'd find a local, positive based trainer who can come to the house and watch the dynamics between Piper and the kids and give you pointers on dealing with it best. I bet it wouldn't take more than a time or two for a good trainer to give you the help you need to manage this.