Howdy!
Julie, we lived in Dallas at the time of our first European trip during July and August - during a +20 degree F heatwave. But the lower humidity felt sooo great! Now that I live in N. CA where the summer weather may be 100F+ but 15% (or less) humidity, Europe feels.so.humid :-( And you already know how Texas feels. Even IF you live in Austin! Gig 'em, Aggies!
Anyhoo...this is a hard call. The taxi boats in Venice can be packed during the summer; they can be worse than the actual sites :-( But you're in Venice to see The Biggie Sites, so it will be hard to escape the crowds unless you hit the big sites very early or late in the day. There is an incredible amount of day trippers there from cruise boats, etc., so anything you can do early or late is better. As already stated, the huge crowds are mostly around St. Mark's, so with little effort you can escape the throngs. And I LURVE Siena! Lurve it! But probably No Palio for your daughter, and probably not for me, either. I don't want the extra crowds for a 4(?)-minute race. Siena has crowds, but in my experience it's nowhere near as bad as Venice. The main crowds in Siena seem to be in the 'inner ring' street just above Il Campo.
But...Venice is Venice (sigh)! I'd hate to ever give up Venice!
Would you arrive at the lodge by car or by train and taxi? The lodge is not close to 'central' Siena, but I see there is a bus stop nearby and of course taxis are available (and quite The Sienese Experience!) so you could get to and from Siena.
There are other accommodations in Siena (I know, I know, you love that lodge!), so maybe you can work Siena into your plans without cutting one of the other locations. Your family might find 4 nights there about 2 too many if they aren't really interested in history, architecture, etc. While you're in the orangerie and taking cooking classes, what are they doing? They may not like that much swimming LOL! Four months there aren't too many for me, but...that's me ;-) If you choose another place in Siena for, say, 2 nights, try to NOT be there for July 2.
I don't know if forming a 3-person 'cocoon' around your daughter to provide a bubble of personal space helps her at all in crowds, but I'd sure like to have one ;-) I don't like The Crush, either.
Your family will just have to watch some travel videos to make a decision. In case you don't own any or haven't yet found a link to RS' videos, here is a handy link. You can watch 2-4 minute clips, or entire episodes. Happy Decision Making!
Bye, Y'all! Go have a Dr Pepper for me...