Since Supergirl will be paired with Arrow on Monday for the Mega-Crossover, it has to start with Supergirl's world. I think Supergirl, Mon-El, Martian Manhunter, and Winn may be the ones from
Supergirl to crossover. I don't know how Alex will take to the idea of crossing over to another dimension.
I don't see why Alex would have a problem going to another Earth. She had no hesitation going to another planet using the transmatter portal in S2E9 "Supergirl Lives". Alex is a scientist and in her own way a nerd so she probably gets the whole multiverse thing like Winn did in S1E18 "worlds finest". Kara trusts Barry, Oliver, Cisco and everyone else on Earth-1 so that will be enough for Alex to trust them too. She may be mad at Oliver for being a jerk to Kara but since Kara ultimately worked things out with him Alex will be fine with him.
Hope, Help and Compassion for all