Not sure why someone said that is separation anxiety. I've been through it and from what you wrote it just sounds like you may need to get more aggressive with housebreaking 101. Are you using a crate? Basically make sure she goes after sleeping, shortly after eating and don't leave her out of your sight if she hasn't gone for a while. You can figure if she has gone, she should be ok to roam the house a bit, but if she hasn't you may be taking a step backwards (and into a wet spot). Praise her like crazy after she goes outside. If you ever catch her going, give her a stern NO! and run her outside. She should learn going outside is GOOD and going inside is BAD. Is the flap like a doggie door? If so, you may want to put a bell on it so you know when she is in or out to reinforce the behavior. As far as the rain…. well, yeah that is a never ending problem. Basenji's sure hate rain. I have to walk out with mine and keep tossing them in the grass until they go, then give them tons of praise when they do. I've been putting up with that for 13 years. Your idea of walking in the rain is good. Keep it positive. Negative associations are hard to overcome. Good luck.