Hey, Walt! Sounds like we'll be visiting the house of mouse around the same time. I've been to the parks several times during the week following Thanksgiving (I arrive on Saturday after Thanksgiving, leaving the following Saturday), and have done the
MVMCP a few times. Here's my thoughts, based on a few experiences:
Any time you can avoid a weekend, do so. Generally speaking, the parks tend to be crowded on the Saturday after Thanksgiving, less so on Sunday, and much, much less so by Monday (Sundays can still be crowded because some folks opt to leave either late Sunday or wait and travel on Monday to avoid the post-Thanksgiving masses who travel on Sunday).
My vote would be for the Tuesday (in fact, that's when I bought my ticket for). I would expect it to be quite a bit less crowded than Sunday.
As for rain... I'm afraid it's a "rain or shine" kinda deal. If you buy a ticket and it rains on Tuesday, they can't let you go on Thursday because those tickets have already been sold, and that day may actually sell out. So it's sort of a "cross your fingers" kinda thing, or, as they say in Vegas, "roll the dice and take your chances." The good news is: I've never had it rain during my post-Thanksgiving week MVMCP. That's not to say I haven't gotten rain during the week... my pal Betsy and I spent a day in a steady rain over at The Animal Kingdom (it was actually quite a bit of fun... felt like we were really in the rain forest!). But it's never rained on Mickey's Christmas party. At least not for me, not yet!
Richard