I traveled to WDW earlier this year with my family and met my parents
there. My parents were staying under a separate reservation. We made a
request to be placed near them in the hotel and, as we asked, they were
given the room directly across the hall from us.
Making a specific room arrangement request such as yours is a two-step
process. The first thing to do is call Disney reservations
(407-W-DISNEY) NOW to have your request added to your file (do not wait until the online check in to do this). It doesn't
matter that you are traveling under separate reservations, just give
the reservationist the names of the other members of your group and
your request for connecting rooms. You may also want to have your cousin call to make similar requests so that the notation
is on everyone's reservation.
Then, you'll want to follow step three on Bret's answer about room requests
HERE.
Confirm your request with the hotel directly about a week in advance of
your arrival. (And also note it on you online check in form.) If it is at all possible to accommodate you, Disney will.
Have a wonderful visit to WDW!