Yes, they are very good at getting to the other side of the gate. Mine used to do that when she was 12 to 13 weeks old but she climbs out instead. She doesn't do that any more as she had learned that I wasn't happy about it. She just wants to keep me happy I think.
I heard the type of gate you are using is not safe (the wood cross crosses and makes little diamond shapes). They could get caught in the diamond and hurt themself. If you are going to get a mesh to put over it, please make sure she can’t chew thru it. Yorkie are very good at chewing and I have seen them in action.
Otherwise, if you want to get another gate, the one I got (from Wal-Mart in baby section) is called “Supergate III “. The opening is small and it could be used as a pressure gate or you can mount it up as a swing gate if you wish. It is 28” tall I think and the price is very good by the way.
Good luck with your little one. I bet she would stop “breaking out” if she knows you don’t appreciate it.
