mySQL - using same db for two domains

Hope someone here can help me with this, because my ISP can't!!

I have a MySQL database set up for domain one, which I also want to use for
domain two. When (using PHP) I try to connect from domain two, I'm told that
access is denied (using domain two's user name and p/w) or just nothing
happens (using domain one's). Is it possible to set the permissions so that
domain two does have access rights? If so, how?

Bearing in mind - I don't have telnet access to this server.

TIA

Sue

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