I am going to respond to this with 2 views, one is as a pediatric nurse, the other as a mother.
First off as a pediatric nurse many parents want their children tested for things all the time. I am not saying that you are like this, but I do want you to understand being tested for diabetes can be difficult on a 3 year old. It would first include lab work. Depending on the results of that they may be required to take a glucose tolerance test, similar to the one you had when you were pregnant. If the only signs she has is thirst and frequent urination I do not think you have anything to worry about. If she is not over weight or loosing weight the thirst could just be that she is thirsty and the urination just that she is drinking more. You cannot compare how much she drinks to how much your other child drinks, every child is different and how much she is drinking could just be her, but if it has recently increased and she is drinking a lot of water and not juice then you might need to be concerned. The accidents may not really be indicative of diabetes, this could just be she is busy playing and doesn't want to stop, or she is acting out. This could also all be because of a UTI, if she complains of burning or if she only goes a little bit when she does go to the bathroom, then I would have her urine checked first. If you are concerned here are some signs you should be watching for: weakness or fatigue, extreme thirst and dehydration, frequent urination, abdominal pain, nausea/vomiting, weight loss, or fruity smelling breath. Of course if you are concerned I would talk to your pediatrician, he or she can give you better advice on if your child is at risk for diabetes.
Now as a mother I say get her tested. I have diabetes on both sides for my daughter. Both my father and and father-in-law are insulin dependent diabetics. I know that the test includes getting lab work done which can be difficult on both mom and child, but if she were showing signs and symptoms I would want to know and not worry. I will not however, just have her tested just to have it done.
The best thing you can do is stay informed and know the signs of diabetes. I hope this helps, and let us know what happens!! Good luck!