If the client doesn’t want any links directed to either of your sites, respect their wishes. Whenever I see a designer’s or developer’s name on a client’s site, I feel it makes the whole thing seem of less quality. Of course that’s just my opinion. It’s also typical for a developer to just add his/her info in the development files anyway.
Now, about your payment issue, that part seems entirely your mistake. You clearly need to tack on any fees whether it be for taxes or Paypal. You also should never send over anything before payment is received otherwise you’re vulnerable to these types of issues.
Best of luck.