Whenever I have seen this language before it has meant that the player in question owes money to stars, often from credit card chargeback(s).

This.

So you didn't have an account on Stars in the first place and you said you MIGHT give them a try in the future. And then you also say this a very serious matter and means a lot to you. That doesn't really make any sense. How can it be that big of a deal if you had never played there before? Also if I know anything about Stars it's that statements like this:

"I wouldn't be able to live not being allowed to play on the biggest Poker site in the world. That's too much. I have done nothing wrong."

will have a very negative effect on whatever you're trying to argue. Stars is very wary of anything that can be interpreted as a suicide statement.

Overall something is incredibly suspicious here...

Haven't read all the emails so maybe it is already answered but why does it say your son and you are saying your cousin?

This is wrong. They can refuse business to anyone without reasoning, therefore no one is entitled to play on Stars.

Also, there's obv some convo missing between this...
...this...: ...and this:

So someone that lives at your house created an account, broke enough rules that he's banned forever, and shortly thereafter, someone tries to create an account from the same house under the same name.

Even if everything you say is true, it still wouldn't make sense for them to allow you to play (which they have the right to decide), given that there's no way for them to know for sure.

It's mentioned in the emails. PokerStars made a mistake.

I wonder what account issues are unresolved. Sounds like your Cousin owes Pokerstars some money. You better figure out what he did.