We went to Mt. Vernon with our older son when we visited him last Spring and we really enjoyed our time here.
The grounds are quite expansive and in better weather, you can tour the house, Working Farm and Gardens, worker housing, Blacksmith and other shops, Barn and Stables, Distillery and other buildings that comprise the whole of the estate that encompass the entire Washington Estate in Mount Vernon. If you just want to 'walk through' - there are small placards mounted everywhere that you can read in nearly all of the buildings. Maybe 2-3 hours at a brisk pace to see these if you work at it.
However, one of the key things we did was to take the Tour of the Main Mansion and Grounds which has a ticket cost of $26/adult (age 12 and up), $13/child (older than 5). There were also separate free (and paid) tours going through various topics including a visit to the Distillery and Grist Mill (free with Grounds Pass) which were a short drive at another place where a short tour rounded out our visit. If you don't take these tours, you will have a much shallower experience of visiting Mount Vernon although if you have younger kids with you, you probably have to weigh what you can handle with the more extensive touring guides. These 'core tours' really bring the Estate to life as the docents who are expert in the grounds and buildings can give you the history and do Q&A with the small tour groups (about 10-12 people at most) and this adds a lot of richness to your experience. There are audio tours that you can also 'check out' to do your own walking tour but we found the personal guide we had to be really strong in her story telling which helped a lot.
In the end, we spent more like 5+ hours in total and didn't even really cover the museum as thoroughly as we would have liked about slavery on the plantation and how the story of Washington releasing them came to be. It's truly quite an experience to see not just the furnishings and facilities but to understand the way of life the Mount Vernon came to represent as Washington took ownership of the farm, transformed it from just farming into distilling and fishing to pay for its upkeep and to then free the slaves that he could because he realized it was the right thing for him to do as the founding father of our country.
Bring suitable clothing, walking shoes and munchies, although there were tables and an onsite 'cafeteria like' food truck setup on the grounds when we visited (outdoors, not indoors), with picnic benches. Just remember, you are walking all over the place, on well-groomed rolled earthen pathways, and some bricked paths, except for the floors of the buildings themselves. One thing, we were fortunate to be here on a less busy weekend day, versus competing with a school tour, which I read in other reviews, which I think would impact getting through your own tour if a large group is there at the same time. My own view is get there early when its quieter too and the staff are fresh.
If you take your time, you will have a great experience.