Whilst you are correct about cheap getaway weeks being available, if the stay is only two nights it may not help too much.
Anyway here are some examples for September: -
Marriott Grand Chateau - Sep 17 - Sep 24 studio up to 4 for $303.00.
The Villas/Suites at Polo Tower - each week in September 1 bedroom up to 4 for $445.00.
The Jockey Club - 1st and last week of September 1 bedroom up to 4 for $445.00.
Those examples are II Getaway and in Australian dollars, though they also need the guest cert so add another $40, not that much difference than renting 2 nights directly off Marriott, but if they have a Gold II member that evens it out. If they are having to pay $60US for the 2 kids plus an expensive rate for the Saturday night at a casino even if they can get the Sunday cheap, $303AU isn't much more even if it is just for used for 2 nights.
I've stayed, Excalibur, Mandalay Bay, Marriott Grand Chateau, Wynn, Jockey Club, I'd recommend Grand Chateau over any of them, particularly with kids and some of the mini-bar displays charging you as soon as the item is picked up, I'd hate to have kids in a room like that.... (that would be the Wynn...)
The Gold II short break exchange might also be available, depends on how much someone would charge for the exchange, though they are a minimum of 3 nights (?? I think ??), but that would probably work better with not having to worry about arrival time....
Sunday to Thursday you can get ridiculously cheap accommodation in Vegas, particularly with the 'current economic climate', Friday and Saturday, the CEC is hardly a factor and rates go up dramatically, Nov09 Excalibur was $19 per night Sun-Thurs and $150 per night Fri-Sat.