At this point I would suggest therapy for yourself and the girls. A therapist for you would be able to help you in your parenting and decision making processes. A therapist for the girls will be able to get to the root of their problem and fascination with diapers and touching. Your children should be in no position to question your decisions or negotiate with your rules.
They should not be touching each other and especially not other peoples children, NO EXCEPTIONS. This is not a negotiation, they are children, you are the adult. Their reaction of trying to kiss each other is proof that they are not taking you seriously. You have to decide on a form of punishment, and when they do these things, they must be punished consistently.
I have asked a few other people for their opinion on the diaper vs age question, and everyone I spoke to agreed with me, there is NO reason for a potty trained child to be put in a diaper or pull up. There are some children who wear pull ups to bed because they wet the bed, but to put diapers on a child for a trip is just irresponsible and lazy. Why is heavens name would your sister put a diaper on a 13 year old child? Because they don't want to stop as much???!? So, subject the child to the humiliation of soiling themselves, and potentially cause emotional damage, so that you can get where you're going faster? That makes no sense to me.
If the girls had potty training issues when they were younger, that's one thing, but at that age pull ups were really the only appropriate response. Not diapers.
I cannot agree with what your doctor said. A family doctor may not be equipped to deal with mental issues and should simply refer you to a doctor who can deal with those issues. I absolutely do not believe that you should be negotiating with your girls on these issues. Giving into them will only show them that they can get what they want by behaving badly. It's setting a disturbing precedence.
Seek help from a family therapist, someone who can treat you and your daughters, separately and together.