My puppy is now 15 weeks old. Even now we take him out every 20 minutes to half hour. Usually he does urinate when we bring him out, but sometimes it takes a few minutes and there isn’t much (I think he’s peeing just because he knows we expect it, as we put him in a pen outside any time we expect him to pee). Other times, he pees for what seems like a forever. And yes, there are times he pees twice within 15 minutes or so, especially in the morning. He rarely sleeps more than 2 hours at a time in his crate during the day without needing to go out. By 10 weeks or so he was sleeping through the night (from about 9:30 to about 5:30). So... A lot of what you’re describing seems to be within a realm of “normal” based on my experience. HOWEVER, the peeing small amounts at a time in a brief period sounds like a UTI to me, especially if she has a history of UTIs. She may need another round of antibiotics, or they may need to do a cystocentesis (remove a sterile sample of urine directly from the bladder with a needle) to be sure of what bacteria you are dealing with so they know they are using the appropriate antibiotic.