How to teach Puck the difference between his toys and a child's toys

Hi guys!

I'm hoping to get some advice from everyone, especially from the moms of human kids or people who have their pug around kiddos a lot.

I babysit for a 3 yr old girl, and her parents are nice enough to let me bring Puck over with me They have an older yellow lab that gets along with Puck really well and the little girl does great with him. She loves it when I bring him over and she is always very very gentle with him. The two problems we've had are that he barks...a lot.. but we've solved that by bringing his squirt bottle along, and the fact that he tries to eat/ play with all her toys!

She's only 3 years old, so she's kind of messy and although we work on picking up our toys when we are done playing with them.. it doesn't always happen right away. When Puck comes over he always thinks all those toys hanging around must be toys for him. We don't have kids and the only things that are on the floor here do belong to him, so I understand why he thinks that (he's a little spoilied at our house..). How can I get him to understand that at her house those toys aren't for him? She gets really upset when he starts chewing on one of her toys.

Also, he's really really bad about thinking if a kid has something in their hand, then it is for him. He'll run over to them and try to jump and get it out of their hand, and since most little kids get excited and yank whatever it is away, he seems to think they are playing a game and keeps at it. I keep him on the ground and don't let him jump (when he's on his leash) but he still gets exited and seems to feed off the kids energy. I try to explain to them that when they get excited and wave around whatever is in their hand like that then Puck thinks they are playing a game and will try to get it. But its hard when they aren't my kids, I feel akward trying to correct the behavior of a strange kid. It is a little better with the girl I babysit, since I'm actually in a position where she listens to me and I'm around her enough to reiterate my point. She has gotten better about staying calm-but it still happens sometimes.

Puck is awesome with kids, he loves them to pieces and gives them all kinds of love and kisses and I know he would never hurt them on purpose. He just still has A LOT of energy (he's only 1) and besides going to babysit with me sparatically he doesn't interact with kids for more than a couple seconds when they pass by. I guess the question I'm asking after my really long post (sorry guys!) is how do I teach Puck that not everything is his? That those toys on the floor of her room are not for chewing and that he CANNOT jump after something in a child's hand?

Thank you guys! Sorry again for the long post.