Of course there's a rule! In this case "to be happy ABOUT something" means "at være glad FOR noget". That's why you have to say "Jeg er glad FOR at se dig = I'm happy to see you".
On the other hand, "to look forward TO something" means "at glæde sig TIL noget". So you would have to say "Jeg glæder mig TIL at se dig = I'm looking forward to seeing you".
Same applies to other prepositions.