Puppy jumping on kids/tugging their clothes

I've searched through posts here as I know this is a common issue, but I'm not having much success from the methods I've seen suggested. We have a 3 month old puppy who has really taken an interest in jumping on my kids and biting/playing tug with their clothes. She does attempt the same with my husband and I, but we just turn around and ignore her, or tell her "off" (which she knows), or if she's biting my clothes I gently but firmly remove her mouth from me and then walk away. But, my kids don't do any of these things and puppy seems to target them. My kids are 6 and 9, so they are well beyond the age where I can just keep them separate from puppy all the time. They aren't ever alone with her, and we have baby gates up. But, as puppy is still housetraining I have to be watching her constantly, so I can't just plop her on the other side of the gate and ignore her for long. And my kids are old enough that they walk around the house freely opening/closing the gates on their own. We've tried teaching the kids to turn and ignore puppy or remove her mouth from their clothes. But, instead they usually just stand there crying or upset waiting for me to intervene 🤦🏻‍♀️ If puppy is being jumpy, I will hold her or remove her from my kids. However, what happens most often, is that puppy was calm and then my kids walk around and puppy hops up from whatever she was calmly doing to go chase my kids. We've done practice sessions where we have the kids approach her and wait to per her until she sits, and give her treats for sitting. She does this well when she's calm. But when she gets hyper, all bets are off and it's like she sees my kids as a moving target to chase and chomp.