My husband and I are coming to the US with our 2 children - 13 and 10.We will be in Jackson Hole and have 3 days before our next stop in LA. We would like to hire a car and see what we can of Yellowstone. Can someone suggest the best route and accommodation which will include the sights and not get the kids bored?

Your question says to me that you should go elsewhere. If you have children who are going to be bored with Yellowstone then why go? Find a motel in Jackson that has a swimming pool and stay there. There are more attractions in Jackson than in West Yellowstone.

Hate to sound perverse, but if one of the most unique geologic areas in all of the world in and of itself does not interest the children, the primary reason for being there suddenly disappears.
Who the heck wants to wait hours to see water spurt out of the ground? And your chances of seeing a bear are low.
Most of the park is just a lot of burned trees. (Most of the snags from the fires of 1988 are still standing. Whole mountain sides are grey because of the dead trees.)
As for routes, there is only one road from Jackson to Yellowstone.
The roads are crowded and some of them are in bad shape -- rough, narrow, and being repaired.
Roughly speaking the roads in Yellowstone are in the shape of a figure 8.
On the east side of the park is Lake Yellowstone, with a road that leads north to the Falls of the Yellowstone and the Grand Canyon of the Yellowstone. (The canyon walls are this incredible yellow and red rock, and the falls are gorgeous.) From Canyon, drive across the middle part of the 8 to the Norris Geyser Basin, then south to Madison Junction and on to the geyser basin where Old Faithful is located.
It spurts water and steam every so often on a fairly predictable basis.
(Old Faithful is the most predictable geyser in the park, but it is not the most spectacular. Grand is the grandest, but it is predictable only within a 4 hour time window, so seeing it erupt requires waiting which is usually very boring. I only saw it 3 times last week.)

From there, back to Jackson.

I doubt if you can get accommodations in the park at this late date unless you luckily find a cancellation.

If you don't want to go back to Jackson, there are motels with swimming pools in West Yellowstone. I like the Fairfield Inn and the Kelly Inn. (Same owner; good facilities, better amenities than anything in the park.)

If you are planning to stay in Jackson for 3 days ..you will be in for quite a bit of driving to see much of the Park. Although in one long day of driving you can take a whirlwind tour of Yellowstone..I have made the drive from Jackson up thru the Park and back several times and it is doable..but you need to like driving. An alternative is to stay in West Yellowstone and drive thru the Park and end up in Jackson. rooms will be hard to get in the Park this time of the year..If you need more information just ask..

if you're staying in the town of Jackson ("Jackson Hole" is actually the entire valley), then you will be in for quite a drive to/from Yellowstone. might I suggest from Jackson, going to the Grand Teton National Park for a daytrip instead. It's closer than Yellowstone and just as beautiful, although it doesn't have any geysers (that's where the water spurts from the ground, as Bob Brown likes to say.) Do your kids like the outdoors/hiking/viewing wildlife? If not, you may be going to the wrong place.

Went to Yellowstone (and many other Nat Parks) last Summer. The only one I will Never Go back to again is Yellowstone, too many people, bad roads. At Jackson Hole you are only a couple miles south of The Teatons, a great park that I will see again. There are some nice hikes, and Moose Junction has a good restraunt.

If I was that close to Yellowstone for the first time, I would go there just for awhile, but you are a bit of a drive from Old Faithful & the Hot Springs area, and Old Faithful is really nothing special the other geysers in the park are more interesting.

But if you just stick with the Teatons and Jackson Hole you will have a good time.