Allergy? Sensitivity? What Is This?

From what I've read, people can't be allergic to chlorine, BUT you can have an irritation reaction to it.
It's technically called an 'irritant dermatitis'.
Does he get a reaction if he swims in a saltwater pool (uses a lot less chlorine)?
He's got to get the chlorine off of his skin - so when he's done swimming he needs to shower off (with soap), wash his hair, and rinse off his suit.
We always do this anyway.
Getting the chlorine off the suit prolongs it's life.
A sunscreen might act as a barrier to keep the chemicals off him while he's swimming but it's still better to wash him off thoroughly after pool time.

He may be allergic to the sunscreen. My two daughters are (and I am too), and the combination of sunscreen and pool chemicals makes it ten times worse. If my kids use regular sunscreen and then go in pool, they will develop rashes wherever the sunscreen has been applied. Your nephew may have no reaction at your sisters because they go in for shorter amounts of time and she doesn't apply sunscreen.

A good way to test this out is to have him use only physical sun blockers for a few weeks and see if the rashes go away. She needs to get a good brand with no chemicals like California Baby, Badger, Goddess Garden or Blue Lizard.

My 6yo son is experiencing the same thing since he has been swimming almost daily. He also has a history of eczema. On the weekends, the rash subsides only to return when exposed to chlorine in the pool on Monday. I am aware of the issue (we cannot use chlorine bleach in the laundry, either), but we just keep it under control with OTC hydrocortizone cream. That does help. We have stronger prescription creams for when it gets out of control, which is not often.
BTW- we have seen the doctor who confirmed it's a sensitivity issue. I'm not going to keep him out of the pool this summer, so we just deal with it. I know it's not sunscreen as the rash appears in areas where no sunscreen is applied. It's frustrating, but thus is the life of the child with sensitive skin.
I would just see the pediatrician, who can prescribe something stronger. I don't think a specialist is required unless the creams the ped prescribes are no longer doing the trick.

It could be the sunscreen.

My kids used to always get strep 2-3 days after swimming in Grandpa's pool. The doctor said that they saw that and rashes alot.

One way to test it is to have him wear a tshirt or rash guard top when he swims instead of suntan lotion, and go for a swim in the late afternoon/evening (so you won't need the lotion). If it's the water, the rash will appear. If it's the lotion, it shouldn't.

No two pools have the exact same chemicals. Even if the chemicals are "the same" in that both your pool and hers use salt or baquacil or chlorine, the concentrations of chemicals vary from brand to brand and formula to formula are different (I currently have three versions of powdered chlorine shock - same brand, different levels of chlorine) and the concentrations of chemicals in the pool change all the time due to any number of variables. You may use different algaecides, different chemicals to balance your ph or alkalinity, one may use clarifier or iron out and the other doesn't, etc.

Allergies and sensitivities come and go - it sounds like with his prior history of sensitivities to detergent that this is some kind of contact dermatitis due to something in the water that's irritating him. If his sunscreen and swimsuits don't bother him at home, it's probably the water. I think she should pursue this with the allergist to see if they can figure out what substance is the culprit. Another option might be a DIY test first - on a day that he doesn't swim anywhere, swab one forearm with some water from your pool and another with water from hers and see what happens. If the arm with your pool develops a rash, she'll at least be able to prove that it's from something in the water and pursue figuring out what specifically is causing the reaction.

ETA: The article references two patients with contact dermatitis that was suspected to be related to pool/spa chemicals. It looks like there is a standard set of allergy tests for pool chemicals, so either the dermatologist or allergist should be able to test for these if it really does look like it's from the water.

Is he allergic to the pool....or the sunscreen I'm sure you're applying each time he swims?

My daughter has one bathing suit that she can't wear. It's a tankini and the bottom comes with reagular bikin bottoms or shorts. She prefers the shorts, but every time they give her a rash on the insude of her thigh. It's the ONLY suit that does it to her. Maybe does he have new bathing suits that are doing it? The fabric of the suits maybe?

could it be the sunscreen? I am allergic to just about all common brands. I have to use the organic type from whole foods. My reaction is that I will break out in a sand paper type rash ALL over if I use brands like coppertone, aveeno, nutragena, bull frog... I've tested each brand and they all do the same. So, see if he could be allergic to the sunscreen.