Yes the land shark phase, not fun! I thought it would never end but he really did just grow out of it eventually. The big thing that helped for us was to always interact with him in a calm way. Don't run around, don't "rough house" (or rile him up). If he starts to be wound up, stand up and step away or soothe with long slow strokes. And yes, those teeth are very sharp. Luckily they should start to fall out soon
I don't have kids so I can't speak to the experience of raising a puppy around them, but I would think that you would really need to work on the being calm part. Yes if they're running and shrieking around the puppy (which I'm sure they are because that's totally normal!), its definitely going to get the puppy riled up. Be calm around the puppy, and if you want to play, put the puppy away in a safe space. Crating our puppy honestly saved me from a mental breakdown haha. It is good for the puppy and it is good for you. It sounds like at this stage unless you are watching the puppy 100% it should be in a crate or gated area. Definitely fully supervise ANY interaction with your kids.
I'm not sure on all the details of the school, it sounds like she is spending a lot of time there. I would say that you should sign up for a weekly (or multiple time a week) class that you take the dog to. This will make sure that she gets some socialization and that she continues her training. As far as the dog park goes, I don't think you need to worry about her hurting other dogs, but I would worry about other dogs hurting her. A lot of dogs give puppies a "pass" for their annoying behavior (such as all this biting!) but there are ones who don't and they have teeth that aren't just sharp but can do real damage. Also at 14 weeks she must have just finished her vaccinations or maybe not be totally done? Definitely not a safe spot for a puppy. I would see if you can arrange playdates with other similar puppies at the school she goes to, the trainers there might have recommendations.
It will definitely get better though! I was still occasionally on the verge of tears over frustration at 14 weeks...and now Bubba is amazing.