kate winslet is 5'7'' or about 1.69m - from this we can see that the door is probably no more than 2m long and 0.75 meters wide, although for the sake of argument we'll simplify that to a 1x2 meter door.
it was probably about 0.08-0.10m thick so in terms of dimensions we've got a 1x2x0.08 = 0.16m^3 door. seawater has a buoyant force of 1065 * 9.8 * 0.16 = 1670 N for a door this size.
the density of the door can be approximated by 600 kg/m^3 (which is the average value for wood). the door would actually be even heavier due to metal ornamentation, doorknobs, etc, but we'll discard that for the sake of calculation. a 0.16 m^3 door would have a mass of 96 kg, or a weight of ~940 N
this means that the door could hold up at most 1670 N - 940 N = 730 N for both jack and rose
730 N is about 74 kilograms, which isn't nearly enough for two full-grown adults