We did Disney 2 years ago - DD was 7. And loved it.
DH and I were both slightly on the "take care" list with back issues - DH is also not a huge fan of big rollercoaster (travel/motion sickness). So I took DD on lots but we said no to a few. And there were plenty that were very gentle. Check the websites in advance - there are LOADS of Disney planning ones.
As we were there for 10 days, we got a 7 day pass (entry into all parks any 7 days in the 10). It meant we could move from one to another if we wanted (so water parks 2 mornings and back into Magic Kingdom or Epcot those evenings to eat and see fireworks, for example). We went into the 4 main parks, but only returned to MK and Epcot, safari one was only ok (but the rangers book, that DCs can get on arrival and get stamped as they go around, was good there).
December is supposed to be the 2nd most busy time - after summer especially around 4th July. Of course, we were there 4th July. But while we couldn't get into MK that evening (mobbed!!), we DID get back into Epcot for the special fireworks night. And got the MK night parade another night. Just be aware it WILL be busy, remember to take plenty of rest stops (including for water) and be happy to leave if it gets too much. Definitely plan on long stops if in all day, but better to have half days (so go in for a few rides and fun in the morning, come out and do something else for a while, and go back in the evenings, or only go mid-afternoon having done something else in the morning). DO remember that you will all need some down time, even adults.
We didn't do other parks (Universal etc) as DD was short so couldn't do most of those. We'll be back again at some stage (DD might be an adult, but we will!!).
But we did go out on a canoeing trip one day down a creek (seeing lots of wildlife, local guide, very relaxed day). And we went to Cape Canaveral to the NASA Kennedy Space Centre - which was REALLY interesting too, for another day.
DD had already flown to Boston via NYC 2 years before, so long haul was fine. Tell the DCs about it in advance, have plenty of distractions ready for the flights etc, but most modern planes (especially if European rather than US carriers - BA and Air France are great) have good in-flight entertainment (individual tv screens in each seat - many US planes still only have over-aisle ones for shared viewing!) and look after DCs well. And you still get fed properly on trans-Atlantic.
It could be lots of fun, and while not summer weather it would still be quite warm in December. But 18 weeks PG means you may be slower, and not fancy charging after the 2 DCs. And it will change the dynamic of the conference as well for you - so bear that in mind, if you are coming back to the family in the hotel every night and not as free to meet with others or to have a drink after a session and having dinner later than planned etc.