You can get a DVC resort - but 2-bedroom are not plentiful period. Your best chance would be in Sept, Oct, Jan, May.
if you are going with school age children - these dates might not be what you can do.
the Marriott are very nice. But being on site is great especially with small children.
if you can afford it - go join
www.tug2.net
It will cost you $15. You are joining for the member only things. the Reviews and best yet - on the BBS board - sighting/distress. sometimes there are DVC resorts listed here.
then go see if you see the same listing. If you can't then your chances aren't good. Some resorts even in the off season don't have enough demand that II will let them exchange into DVC.
however put your request in with II and see what happens. lots of times II will try to get you to expect something else (they get rewards when you take an exchange) - so be sure you get something good - Marriotts.
see if you can't get the information from your mother to register online. Now if she has already done this - then great go look for yourself - if not
http://www.intervalworld.com/iw/cs?a=5
don't mistake the getaways for the exchanges. You must click on exchange (even if just looking) to see the exchanges.