Fletch,
If you cruised Denali then you'll have no trouble with Vinson. Most of the main guides services do it fine, though given the short timeframe of a trip there (c.12 days) sometimes, an experienced guide can make the best decision to work around any weather issues. Vinson is easy until it gets bad - then it gets real bad. Maybe you should climb Vinson soon, as later you'll feel bad spending that much money on something other than your kids
Ama Dablam? Hopefully radson can jump in and give you first-hand comparisons with Denali etc. It seems to be jumaring fixed ropes over all the rock, so not sure how much actual 'climbing' is involved. Note the ropes are there in Oct-Nov-early Dec, not in April-May when the rock is more likely to be covered in snow. Despite the ropes and crowds, it's a natural line up a stunning peak. Relatively safe and accessible, as far as Himalayan peaks go, so possibly a good one to squeeze into a month later when you have kids.
I've been on G1, not G2, though they share the route up to C1. G2 has had a few changes over the years and can be a tough climb, even when mostly fixed. Big Himalayan peaks are quite a different story to Denali, Vinson etc as they really require a decent spell of good weather, which is rare, especially up the Baltoro, and to have enough teams on the mountain to do the work necessary for most of us mortals to climb them. You have the 3rd world travel, hassle and sickness issues, longer timeframe, and even more will-sapping altitude and conditions. Very few guide companies have success on G2, despite its reputation, and so nowadays very few companies go. Manaslu is easier, though more dangerous. Not sure how justifiable any of those peaks are for a family man, opinions vary.
Logan? You can get guided up the King Trench route OK, it seems, though the east ridge is a nicer looking route. ER would be harder than Denali or Vinson, more work, just as cold. I think the KT is not without avo danger. I almost went there this year, but went to Peru instead. Logan KT is relatively quick, cheap and close for you, so another option for later with kids.