It happens many times that 2 verification process happens on the same day. There is a provision in many that one of your parents can do verification on your behalf so I suggest you that you can attend one of the verification with someone guiding you and another verification can be done by your parents. but it is possible that this may not work for anyone of verification. so, according to your rank, you should go to the verification in TS and let your parents go for verification at AP. as you have a better rank in TS and you will definitely get a better college.