How to make entities switch dimension ?

I would like to teleport the player (who is in a vehicle, riding an entity such as a Flan's mod plane), into the End when he reaches an altitude of 255 blocks in the overworld, then the reverse when he reaches the altitude 0 in the End.

https://i.imgur.com/SMoWox5.png

The player teleports fine as expected, when he reaches Y = 255 in the overworld or Y = 0 in the End, but when the player rides an entity, it doesn't work, the player does not switch dimensions.

What should I do to fix this ?