We have a timeshare (offsite) and usually tag 2 or 3 days onsite to our trips. In January we are doing a cruise and are then spending 2 nights at ALK. We like a couple of days onsight to enjoy the benefits of free parking, extended hours, and the total Disney emersion feel. We make those our park days with maybe one other park day during our offsite stay.
I am not sure however if one night is "worth" it. I personally hate having only one night at any hotel unless I am traveling. You may not have the room till 3pm and then have to check out at 11am. You don't even get the room for 24 hours. I would rather stay in the original place for the extra night.
If you do decide to do the extra night at Disney I would recommend go over early in am to check in and then go back to the other place to packup and checkout. You may get into room earlier that way. You may even get really lucky and your room could be ready then.