ME pick-up is usually around 3 hours prior to flight departure...so around 10:30 am for a 1:30 pm flight...
Allowing an hour to get from AKL to Poly makes sense, altho you could cab it in about 15 minutes...but figure about 20 minutes for the bus from AKL to MK...(and allow for 10-15 minutes waiting for a bus during the "opening hours" time frame (which is your likely time frame for a b'fast ADR which you must finish in time to get your MIL back to AKL for ME)...then once at MK, you can see if a Poly bus is there and take that over...or walk over to the Monorail...or even walk over to the Contemporary and take any park bus (Contemporary shares buses w/the MK resorts...I think the Poly is the next stop after the Contemporary)...
Getting there will likely be pretty efficient...it's "high volume travel time" to park openings...getting back might be less efficient...fewer buses "back" to the resorts mid-morning ...
If it were me, I'd make the ADRs for 7:45 or 8...that'll be late enough to allow for Disney transportation to get there, and early enough for stress-free Disney transportation back when you've finished...
Or, if I really wanted to eliminate transportation stress, I'd move the ADR to a different day, or plan on a cab (at least back from if not to the ADR)--
Another possibility worth a phone call: Ask at the AKL Bell Services, or call ME--they may be willing to pick up your MIL from the Poly instead of from AKL... if she can do resort airline check-in, she'll only have her carry-on w/her (if that doesn't include a roller bag, there should be no problem traveling to the Poly on Disney transportation)...
I don't know if ME will do this or not (I do know that roller bags are not allowed on Disney park buses)...but they're more than willing to change pick-up times if someone wants to go early (or later, at their own risk)...so they might!
If you decide to explore this, let us know if they say it's ok, ok?
Good luck!
