Your plans sound great!
I slept at Barcroft Gate in a tent (while my friend chose to sleep in his Volvo station wagon). It is bare, but the sunrise and sunsets are beautiful in a very rugged way. We didn't have a lot of wind when I was there but it is a kind of saddle so I imagine the winds can be brutal. I took Diamox for the first time in my life at that trailhead because I couldn't sleep and realized that I was having sleep apnea (aka periodic breathing aka Cheyne Strokes) -- even having spent the previous night at 10,000', at Saddlebag Lake, as it happens!. But within an hour of taking the Diamox, I was sleeping like a baby.
One other peak hike for your consideration if you don't do Dana -- Mt. Hoffman, off the May Lake trailhead in Yosemite (maybe 30 minutes from Tioga Pass). Mt. Hoffman is only 10,845', and a 6 mile round trip hike (good half day). But the views! It is the GEOGRAPHIC CENTER of Yosemite and there is nothing near it to challenge it for views. So if you want killer views, it is a great option. You are looking down on, among other things, Half Dome and Cloud's Rest, and across the way to Dana, Conness, and all of the high country.
Oh yeah, and the kids can join you for the first mile, and then hang out at May Lake, at the base of Mt. Hoffman.
Here's a link:
http://www.yosemitehikes.com/tioga-road/may-lake/may-lake.htmI'll find some more pics....