Even if you managed to both get a spot at a European or New Zealand university, there is 0.00000000001 chance you would ever be able to bring family unless you found a high paying job and could sponsor them.
You’re trans, and that’s the reason you want to move? Besides New Zealand, have you actually looked into the conditions for trans people in these countries? It’s hardly any different than a blue state, in fact some blue states give you better protections with your insurance on surgeries and hormones. I live in the Netherlands and it’s not as universally trans friendly as you think, and again, fat chance finding housing for a family in a big city.
I feel like people who romanticize migration specifically, and not enjoy the one new country they move to, are the type to never be satisfied. I suppose if you have to skills, money, will power, and lack of attachment to move countries constantly, that’s your choice, but just admit you get bored quickly lol.