Definitely don't do that (putting the money in your account and then transferring it to others). At one point, I was in the process of doing just this and once I talked to Braintree, for example, they let me know how horrible this can turn out to be. They gave me a term for it which I'm now forgetting. In any event, Braintree as the payment processor, also let me know that I'd be violating their terms of use (along with those of PayPal and various other payment processors) if I did process payments on behalf of other people.
Besides being a violation of their terms of service, it leaves a huge liability in your lap. If, as an example, you're taking payments on behalf of Person A and Person B who gave you money to give to Person A suddenly wants the money back that you gave to Person A, how do you handle the case where Person A is nowhere to be found? You're on the hook for that money and now, multiply that over the course of several instances of refunds and disappearances--it could be costly and problematic.
To mitigate this problem, PayPal introduced Adaptive Payments where you can have someone pay you and you share that payment with others. That's one way of dealing with it.
https://www.x.com/community/ppx/adaptive_payments
If you don't have to "touch" the money yourself, there's no problem.