One day should be enough at the MOA if you make it a long day. It depends on whether you want to shop there or just hit the attractions. The kids will like the Rainforest Cafe.
Good indoor attractions for your age children would be the Science Museum of Minnesota and the MN History Museum. They would probably like the elevator ride at the Mill City Museum, but warn them about the simulated explosion. The 11 y.o. is too old for the Children's Museum, unless you're willing to split the family up for a bit (not sure if you have one or two adults traveling). It's a nice museum. The 7 y.o. would like the Minneapolis Fire Fighter's Museum (only open Saturdays, I think, check for sure) and the Jackson St. Roundhouse, but those would be iffy for the 11 y.o. Both would like the Twin Cities Model RR Museum.
IF the weather isn't too cold and the snow is minimal (that's a gamble in late March) try the Hyland Play Area in Bloomington and the free sculpture garden at the Walker Art Center.
We've always wanted to visit the Wabasha St. Caves, but haven't done so. There are some reviews here on TA for that attraction. Maybe someone else will chime in on that.
We stay in whatever hotel meets our criteria and offers the best deal. This varies from year to year, so I can't really recommend a specific hotel. I also don't know your budget. I can recommend areas to stay. Downtown is convenient, but the hotels cost more, parking is not free and you will have to use a bellhop or haul your luggage in and out of parking garages. If this is your thing, stay downtown. There's a nice complex of hotels and an indoor ice rink at the Depot.
If you prefer suburbs, Bloomington is the suburb with the MOA and the airport. The downside is it's also a bit more than other suburbs, although there are some good deals out there. If you can find a good deal, stay in Bloomington. You will also have access to the downtown area via the light rail from the mall. Two suburbs we like are Eagan and Eden Prairie. Both are safe areas, convenient to the mall and airport and less than a half hour drive to downtown.