1) get a good raincoat
2) Walk the puppy on schedule, even if it's raining. FOOD REWARD all outdoor elimination, and use lots of verbal praise. Name eliminations (Go Pee Pee) WHILE they are happening, and food reward immediately afterward.
3) Supervise the puppy during all housetime outside the crate. By supervise I mean if you do not have your eyes ON the puppy, she should be in a safe area like a crate, or leashed to your belt. Use baby gates to keep her in the room with you.
At the same time use the rolled up newspaper trick. It works every time. The very next time you find a spot where she has urinated when you were not looking, take out the rolled up paper, and hit YOURSELF over the head with it several times as you repeat: I FORGOT TO WATCH MY PUPPY.