I did this trek a couple years ago for BACKPACKER magazine. In fact, it was just featured last month in the Magazine. Here's a link to the online trip report:
http://bp2.trimbleoutdoors.com/ViewTrip ... pId=264804
It's a great hike, but Here are a couple of things to consider, especially with he kids:
There is definitely some steep uphill and lots of steep downhill. The main uphill is the trail from Lyell Canyon to just above Evelyn Lake. The trail isn't too bad, but is a steady trek up.
You will be above 10,000ft in elevation so you keep an eye on everyone for the effects from the altitude.
The area around Evelyn Lake is pretty bare. I would continue on to Fletcher Lake if you are up to it. There are some nice campsites among the whitebark pines, plus the scenery of the lake below Fletcher and Vogelsang Peaks is amazing. The disadvantage to this area is the close proximity to Vogelsang High Sierra Camp. However, with the kids this may be a plus having some of the camp amenities around.
The route from Vogelsang to Merced Lake during Late July should be fairly dried out, but there may be a few places where you have to cross Fletcher Creek through "Long Meadow". That is the route I took. There is another route via Vogelsang pass along Lewis Creek, but I haven't been that way so I can't say what the conditions would be like.
The trail down to Merced Lake is fairly steep in places and once you start heading down you will encounter Yosemite's famous granite cobblestone switchbacks. It was pretty exciting to see Merced Lake and Half Dome from above. Look for it and have the kids watch for this view.
The area from Echo Valley to Morraine Dome is one of my favorite places in Yosemite. I call it the Merced River Gorge and the views are breathtaking. I agree with Wickett that it most likely would be too much to go all the way to the valley from Merced Lake. Especially with the mile or so of sandy trail as you approach Little Yosemite Valley (that wipes me out for some reason). I would stop at Morraine Dome or brave the crowds at Little Yosemite Valley (on a positive note, your kids ane girlfired may appreciate the pit toilets). Breaking this up definitely gives you an easier out on your last day. I went down Mist Trail because I really don't like the John Muir Switchbacks from Nevada Falls to the Vernal Falls bridge. They seem to go on forever, plus, there is nothing like Mist trail when the falls are running. Vernal won't be raging, but you should still see some rainbows going down.
Keep in mind that you will be at the tail end of Mosquito season. Depending on the weather, you could be in the middle of it or it could be over. Take appropriate measures and you should be fine.
As for transportation, I recommend parking at the trailhead parking near Happy Isles and catching the hiker's bus to Tuolumne Meadows. The bus leaves early in the morning so you will have to time things just right. There is a cost to the bus. The Yosemite web site has all the info you need on that.
This trip was one of my favorite trips I've done in Yosemite. It is strenuous so you will have to decide whether your group can handle it. Definitely get some training hikes in that includes some elevation. That should help. Also, I take a lot of kids backpacking and I have found some sort of "end of the trip" incentive helps keep the kids motivated.
Good luck and I hope your kids and girlfriend catch the backpacking bug. Yosemite is certainly the best place to start the addiction!
Enjoy!