My roommates's dog did the same type of strange, totally out of character peeing behavior and it turned out to be a kidney infection. He has to take amoxcillin for 14 days.
Definitely check with your vet when you go...they will need to do blood and urine tests to rule out any disease so you may want to give them a call and let them know that you are adding this to your vet visit reasons....
Good luck and keep us updated....

Jennifer & Duncan