Thanks, everybody. I think we're making progress.
Cudedog, thanks for the suggestions. You're right, I have no real history on Scarlett, but she has been to the vet twice in the month I've had her and been thoroughly checked out. The problem isn't so much frequent urination as sneaky, in the house urination. If anything she puts off doing any kind of business until she can't control herself. I've read that dogs who spend long hours in crates or kennels learn to do that. She was in a shelter for quite a while and the more I think about it the less certain I am that the woman who rescued her took very good care of her. .I don't think she told me the strict truth about Scarlett being housebroken. So, we're getting her on a schedule of going outside every two hours except at night. She does fine with holding it from midnight until 8:00 a.m.ish. She has a couple hours outside morning and evening when it's cooler, so she has plenty of chance to take care of business after each meal. It seems that she's on a two hour schedule for everything. I thought dogs eliminated within an hour of a meal, but my two both seem to go about two hours.
At her 2:00 outing this afternoon, she looked at the treat bag, went to her spot, peed and came back to me for a treat, which of course she got along with lots of praise. She wanted more treats, but no tinkie, no treaty. So, brilliant girl that she is she went back to her spot, squatted, dribbled, and then came back to me for another treat.
I think she's catching on.