as others have said you proably can but you will be charged for 2 broadband accounts as the modem is tied to your account.
would be cheaper to run ethernet cable from the router to your daughters bedroom.
is the wireless lan problem a case of a weak signal or just bad relablity? if its reliablity have you tryed going into the router settings and trying a differnt channel, could be interferance from something like another lan, or a cordless phone.etc.
Some routers support WDS (ud have to check if yours does) which enables you to get a 2nd wireless router and use it a bit like a relay station. But both routers would have to support this.
just a few options for you
