Do you think getting another mini will remedy this and eleminate her need to escape?
Maybe, however probably not. Once a horse knows how and where to get out GOOD LUCK!
I've never had luck with electric fence and minis. Try to find a saw mill near by, you can buy 8' wood rails for under $2 a piece in most locations. If you or family members have woods, cut fallen trees that are "post sized" at 3.5 feet length. For about $50 you should have NO trouble making a 3' high 3 board wooden rail fence, 20x20 - put one hot wire around the top so other things don't go in.... This is a cheap fix, if you have the money now make it as big as you'd like, if not as I said $50 could easily make a sturdy 20x20 paddock until you can ad on. At least your little guy is SAFE.