I dont really get what you mean with the bold part of your statement. Do you mean to say transferring money between gambling sites like I withdraw from duelbits and deposit it directly to rollbit? If you say so, I do not think there is a site that restrict such activity because I do not see any reasons why gambling sites restricts their player to deposit from other gambling sites.
I guess it's possible for some casinos to link the hot wallets whenever they withdraw from site to the other but from my experience sending funds directly shouldn't be an issue though it's better to use non custodial for miner fee reasons.
Can anyone tell me how will centralized know that the funds came from a gambling site? I'm only seeing threads before that someone claimed their account got frozen because funds came from a gambling site but no proof that the site itself tells their users that's the exact reason. Coinbase for example but not seeing cases like that in Binance. I think there is another reason why their account got frozen and not because the money was coming from a gambling site.
Because there's a way to track and label the casino's hot wallet for example if you check
wallet explorer you'd see publicly labeled addresses between crypto casinos and other services. What more if there's a paid service that offers more links between casinos.