[The Might]

I am not sure if they really abandoned them. If I remember well, I think I read a bit of the HOME where Melkor first appeared to Men as a great and beautiful lord and deceived them, and Eru later spoke directly to the Men asking them not to listen to Melkor. I am not sure where it is, I am not such a HOME expert. As far as the Valar are concerned, the problem is we aren't given a lot of information on them and the Men in the east, or if any is given, I am not aware of its existence.
One proof that the Valar did not abandon people in the East where Alatar and Pallando who were sent there to help the people. Unfortunately Tolkien indicates they failed in their quest as well.

As far as Numenoreans are concerned I too think the Valar exagerated. They could have allowed the women and children to leave...I can't understand why they didn't. This wasn't just a warning, this was really too much.