Definitely pushing it, even if all flights land on time. I know it is about a 5 minute walk from the lobby at BWV to the back entrance of Epcot. Probably another 10 to get to the front, then a long walk up that ramp to the monorail. As someone else said, can sometimes be a long wait for the monorail. I do love that ride, though, between Epcot and TTC. Anyway, then you have to get off that monorail, walk down and around and up again to the Mk and Resort loop monorail....and wait again.
You mention you will have a PH and stroller. I don't know what a PH is. My idea would be for you to take the Magical Express to the Contemporary Resort, see if you can leave the PH with bell services there, and then walk over to the MK. When done at the MK, retrieve the PH and take the monorails back to Epcot. Although you can't "see" as much if it is dark, sometimes it is really nice to see everything lit up.
I could not give up an ADR at CRT with a four year old. I think she would really enjoy it more than a tour through Epcot. Unless you have other great ADR's planned for your visit. Your niece is lucky to have someone special like you in her life!