I think staying at a hotel closer to Lake Mead sounds like your best option.
My niece lives out there and I've been out to see her twice - once without kids and once with kids (15 & 12). Since we have her to stay with we haven't looked at hotels, but just being down on the strip, I don't think I'd be comfortable staying down there (without kids, yes; with kids, no).
The strip is an event, to be sure, and I do think you can take your children there and enjoy it with them. Here's what we did:
* Parked at New York/New York
* Stopped at arcade in NY for 1/2 hour or so and let the kids have a little fun with a pre-set amount of money. Explained to them just as they blew through $XX in 30 minutes, adults often spend/waste (IMO)far greater sums of $$ in LV gambling. I really think that since they had just blown their money, they had more of a grasp of the reality of what gambling is/does. When they compared the money they spent/lost to what they could have purchased, it all made sense.
* Walked thru NY/NY part where it is kind of like Streets of America at DHS with (indoor) sidewalk cafes, etc that are made to look like the streets of NYC. There is also an ESPN store here. Small, but fun nonetheless.
* Walked outside near the Statue of Liberty and across the walkway to MGM.
* MGM - Lion Habitat and cute gift shop - took pictures with lion hats (plush lion heads that sit on your head - kookie, but cute).
* As mentioned by another poster, there is a Rain Forest Cafe in MGM too.
* Walked outside just down the street to the M&M and Coca-Cola stores. Cute 3-d (free) movie at the M&M store (on floor 3, I think?). Son bought pins at each store (gee, you'd think he was at Disney!

)
* Walked back the way we came and left this area.
* Had lunch at In-N-Out Burger - not far from strip. Evidently this place is an institution. They serve only burgers and fries. Nothing else. Good food, decent prices.
* Went to the Forum Shops at Caesar's. There are 2 shows to watch (free), one near a big aquarium (near Bath & Body Works, I recall) where some animatronic statues come up out of a huge structure and then another show down the mall hall where statues come to life. Kind of fun, somewhat dramatic/Disney-ish. There is also a 2 story FAO Scharwz store. Didn't buy anything, but fun to look around.
* We then drove a short way down the freeway to Las Vegas Premium Outlets. Lots of fun stores, highlighted by a
Disney Store. It's hit or miss, I understand. Food Court had good pizza. FYI, buy a whole pizza, much less expensive than buying it by the slice and with 2 growing boys, it was devoured.

* Back to the strip, parking at the Bellagio. Walked through the hotel, stopping in the lobby to see the colorful glass flowers on the ceiling and proceeded into an atrium to walk thru the botanical garden, which is periodically changed. Both times I've been there it has been beautiful.
* Walked outside and watched the Bellagio Fountains show. We walked entirely around the fountains to see/hear the show from all angles. The fountain shows run all day/evening, but to really appreciate the lights, you have to go after dark.
Hints to enjoying the day
* Buy M&M's before you go down to the strip. You will WANT M&M's after you go to the store and they are much cheaper buying them at a
Walmart or Target.
* Bring Water!!!
* Wear walking shoes!
* Slot machines/gambling tables. We walked past some in various hotels/casinos, but as mentioned by another posted, children can 'walk past' them, but they cannot stop. It is difficult to completely avoid them at times. In fact, slot machines are even in the airport, so best to just tell your kids about them ahead of time.
Instead of visiting the shops, perhaps you could find a little chapel and renew your vows? I think that sounds fun!
We had a very full day, but one day was really enough time to do the things we wanted to do. Other things you could do include going up in the Stratosphere (there's even a few amusment park rides waay up there/no thanks!) and the Shark Reef at Mandalay Bay (but having been to SeaWorld, etc, this had no appeal to us). I've also heard that they've changed the show at Treasure Island. It used to be kid-friendly, but they've changed it back to something a bit more raunchy.
Have a great vacation, whatever you decide to do!