Actually the first reply had it correct.

I arrive LGA at 3:35pm on American and would like to be picked up at LGA and taken to JFK but dropped at the hotel right by the entrance to JFK.

I don't know if EK will accept any place other than JFK as the drop off point.

If not, I guess I could ask the driver if he could drop me at the hotel or worse case just get dropped at JFK and take the shuttle to/from the hotel.

The next question is whether they would allow a pick-up at 3:35pm. Would they consider that too early for an 11pm flight?