I think she is a keeper and a precious little soul you can work through issues. Two amazing hurdles you don’t have to deal with, she likes your other dog and she isn’t terrified by men (making an assumption here BH :-) That is a huge starting point. Peeing on the rugs….can you gate her to the tile areas and put pee pads down to start with? There are a number of break in routines for new dogs but I think you are past that. Has she made you her primary person? Make sure your wife does important stuff like feeding so she doesn’t get possessive and protective of just one person. Good luck and keep us posted! If all else fails there are rescues devoted to these situations and will do good by the dog.