Hello, Christina! Thanks for letting us help you in planning your upcoming Walt Disney World vacation.
I will say this -
Be Our Guest Restaurant is a spectacle to behold. The theme is carried through to every detail, and the rooms are absolutely stunning. If you have the opportunity to enjoy a meal there, go just to get a glimpse of the interior of the restaurant.
Now, having said that, there are no characters at the restaurant at lunch time, and I would say the transportation time back and forth between the Magic Kingdom and Epcot may cause you to lose up to two hours of your theme park day (I always say plan 45 minutes to an hour in each direction). The lunch options at
Epcot, especially in the World Showcase, are incredible, and as awesome as the theming is at Be Our Guest, there are some dining options that offer truly delicious meals at Epcot.
Taking everything into consideration, I just can't see taking up precious theme park time in the transportation, unless you plan on spending the rest of the day at the Magic Kingdom. To go there, eat, and come back can be exhausting for little ones, and I would say that you would make much better use of your time to just find a great place to eat at Epcot.
Oh, and keep checking
Disney Dining Reservations for the possibility of a cancellation on a day that you will be at the Magic Kingdom - or at the very least hopping there for the morning or afternoon. You may luck into a breakfast or lunch cancellation that you can take advantage of.
Happy planning, Christina!