12-Week old Beagle pees in crate

[SealingWax]

Hello, everyone. I have a question about our new little girl, Maisy. She's 12 weeks, a Beagle, and a darling. But she has no problem at all peeing on herself. I've read and read that dogs WILL NOT do this, that they want to keep their bed clean. Maisy will pee any time, on the floor and things, which is normal when little, but that she goes in her crate every time we put her in there is driving us all to drink (even the 9-year-old, but she drinks tea).

I've:

1. Restricted her water after 8:00 p.m.
2. Set the alarm for every 3 hours at night to take her out - sometimes she's still dry, a lot of the time she's wet her crate (with a cushy beddy thing in there or nothing at all between her and the crate pan, it doesn't matter a bit).
3. Never left her in there more than an hour during the day.
4. Fed her on schedule (9 a.m., 1 p.m., 6 p.m.).
5. Never punished her for messes, since I don't catch her doing it.

She never poos in there... WHY does she know to hold it for poo until I come to get her, but doesn't care a bit about urine?? I'm going stark raving mad. Please help!