If you skip MV then your drive is less than 4.5 hours. Add 30 minutes if you go via Monument Valley. Add 1 hour for lunch. So your driving is 5.5 or 6 hours, depending on which way you go (maybe less).

If you leave at 10AM you could get to Tuba City at 2:30 and spend 3.5 hours seeing the sites of Tuba City and then it would be 6PM

Or, leave at 10AM, spend 3 hours at MV, and arrive in Tuba City at 6PM.

The only question I would have is: should we stop at Natural Bridges in addition to, or instead of, Monument Valley?

p.s. I don't know what they answer to either of your questions is. I am interested in an answer to your first question (our decent lunch will be in a cooler in the trunk).

Monument valley can be long or fairly short. As with most of the other places I suppose the more time you spend there the more you get out of it. Our first visit we spent about two hours between looking from the view point, checking out the gift shop and deciding we would drive ourselves around the valley loop. I wasn't all that impressed with the valley loop, just the same thing from a different direction.

So the next time we went we just took a look from the viewpoint and called it good.

I believe the valley tours are about two hours so if you wanted to take one of those you'd need the time. The backcountry tours are supposed to be better, but I've never had the money to pay for them and with a family of four it would add up. Can't say if it would be worth it.

So I guess my answer to your first question is Yes, there is much you can see at MV in less than an hour and a quick stop imo would be worth it. Then if you decide to spend the extra time with a tour you could make that decision right there.

Second question. Define decent I'm with mrwunrfl. We have a cooler and there is a picnic table by the viewpoint. It would make for a great picnic spot (as long as the wind isn't blowing).

Third, to give you my opinion about whether to do Natural Bridges or MV I'd probably do the 1/2 tour of Monument Valley. Other places you might want to consider stopping along the way (at least in Utah, can't give much info about the Arizona/NM part). Edge of the Cedars in Blanding is a great little museum. Twin Rocks Trading post in Bluff and San Juan Trading Post in Mexican Hat, both have some beautiful buys. The Bluff historic fort has some interesting stories about the pioneers who first came into the area.