Sorry to say, but you will have this problem (going to dad's and having to "train" all over again when she returns) for years to come... not speaking of the potty training only. My daughter is 6 and every time she comes home from her dad's we have to remind her what our rules are. It usually takes her about 2 days to adjust back to our norm. It's just a part of life and you will have to adjust to it as well. You can't change what goes on at dad's, so don't try (it will only cause conflicts!!!). We also have the same problem with my step kids, when they come for visitation we have to remind them of our house rules. I know she is only 3, but try talking to her before she goes to dad's. And remind her of what is expected as soon as she returns. Structure is so important for kids... make sure you establish it at your house.
Also, I agree with the lady who mentioned the panties. We had the same problem with my daughter (only at night time). As soon as I started puting her in bed with panties she stopped having accidents.