The Vidanta resorts in RCI include the following in the urgent information part: "Multiple and consecutive reservations must start in the same day of the week." (That's from the Grand Bliss & Grand Mayan NV, Grand Luxxe, when available through the platinum priority access part of RCI only allow one stay per year per type and leave it as a bit of an open question whether switching room types (i.e., resort ids) would have the same requirement.) I'm not in II, so couldn't tell you what type of limitations they have. If it were me, I would contact Vidanta Customer Service (800-292-8446 U.S. or
CustomerService@Vidanta.com) and ask them, or at least let them know you're not checking in on the first day of the second reservation, if that's how you do the switch.
The one thing I'd add to what Phyllis said is that they won't give you the second room until after 5:00 pm (or fairly close to that) on the day you check in to it. You may be best off checking out late on the 6th day of the first week from the first room so you can avoid being in limbo for the day waiting to get the second room. Otherwise, keep your bathing suits out of the luggage when you move and spend the day at the pool.
The other option you'd have is to volunteer to downgrade to a 2 BR for the second week in order to avoid moving. They might let you do that when you check in if they've got the spare capacity, which is probably the case that time of year, so they can use the 3 BR upgrade as an inducement for someone to go to a sales pitch.