By all means take her in for a checkup to rule out a UTI. However, the peeing patterns you are describing (peeing for corrections, peeing when greeting new people) sounds to me like submissive urination - she is peeing because she is afraid and wants to show you/others she is no threat.
Being a rescue, it is very possible that she was punished for peeing or other "undesirable" behaviors and has this has developed into a strong fear response.
What type of training methods do you use? Positive reinforcement training is a great way for shy dogs to gain confidence in you and themselves.
With many fear behaviors the best strategy is re-direction. For example, if she is urinating when new people come to the door you can teach her a place command in another room and wait until your guests are sitting down and less threatening for you to introduce them.
Let us know how things are going