Hi! Welcome to YorkieTalk!
I am one of the "tiny" Yorkie owners with 3 kids ages 6, 4, and 3. Your kids sound like they are already following the same rules that I enforce with my kiddo's. I am a fairly new Yorkie owner, only had Missy for 3 months now, but I have to say that things are going FANTASTIC with how my children treat her. They don't run in the house, they make sure their toys are always picked up. They are only allowed to hold her in their lap while sitting on the floor, never while standing or walking or sitting up on the couch. They have understood completely since Day 1 how to treat Missy. They are very gentle with her, and they make sure she never gets into anything that she shouldn't. They are always making sure that Missy is safe.
As far as Yorkies personalities, they are all so different! They are suppose to be hard to potty train, my Missy has been pee pad trained since coming home at 7 weeks old. I can count on my fingers how many accidents she's had in the house. She's been great from the start, thanks to the breeder starting her in an ex-pen with pee pads, crate, food and water. I just continued doing this at home until I was comfortable giving her free reign because she was being so consistant with her pad. She *rarely* barks. When she does, it's in play and very quiet. She only chews her bullysticks. I can leave her alone in my house at 18 weeks of age without her doing anything other than sleeping. I'm aware that things could change in the future, but so far until she messes up, I'm giving her the benefit of the doubt. She likes to be with me every moment of the day, but also doesn't seem to mind when I leave. She just sleeps. Also, I've heard that Yorkies are usually only a ONE person dog. This isn't the case with my Missy, she loves everyone in my family of 5.
This is my first Yorkie, and I am really impressed with the breed. I already want another one. They are so intelligent!