Awww, the "can we go home now?" picture is so sad. You can just see it in his face that he's had enough. Poor boy.
Maybe you could just do play dates with the dogs on neutral grounds at a dog park. Then perhaps they would become friends. This is if Lizzie gets along with other dogs. I mean, obviously she does or you wouldn't have taken Taggart over there at all.

Hey Taggart, you can come to our house anytime. My two will be nice to you and share all their toys and the big backyard with you. Zoee will show you all the squirrels and Taggart will play chase with you. Hee hee