Ask for a recommendation letter from a teacher in the university I'm applying to
I doubt that the letter from a professor at the other university, especially if just "okay" is going to help you much, if at all. If s/he writes you a letter, ethics might require that they can't participate in your admission in any other way. I'd suggest it is better to get good letters from those who know you well, and if the other's remember you positively it will just be an added bonus. 

Of course, if someone knows you, they might also be limited in how they can participate, depending on the nature of the rules in place.