Help me with house training!

I have a 4-month-old Havanese female who is very smart - you don't have to tell her most things twice! I know she can't be completely house trained yet but...I've tried crating her when I leave the house (never for more than 3 hours and usually less). First, she figured out how to open the crate. The breeder suggested I bungee cord it closed so I did. She peed in her crate both times I did that and was totally stressed out. Then I tried confining her in a bathroom with a gate. She figure out how to open the gate. So I turned the gate into a pen (it's one of those 8-piece fences that you can assemble many different ways). She can jump over it. So now I'm leaving her out. She doesn't always pee and when she does it's almost always on hard floors but I'd like to get her away from doing it inside at all, particularly since she's really good about going outside - gets a treat when she does it. Any ideas on how to wean her from peeing in the house?