"After my stay in Israel, I decided to go
through the formal conversion process. Now that I've done so, my status
is that of a new-born person, with none of my previous family relationships.
Doesn't that mean I should cut off all contact with my non-Jewish mother
and her non-Jewish influence?"
Let's not be too rough on your biological mother. It is true that you
no longer have a Torah obligation to honor her (1) since, as you said,
you are like a new-born, so technically the old son-mother relationship
no longer exists. But this doesn't mean that in her eyes you are no longer
her son. She still cares about you very much, and you still owe her gratitude
for giving birth to you. When you were a non-Jew you were still supposed
to honor your parents, right? For that reason the Rambam writes (2) that
a convert is forbidden to abuse his non-Jewish parents and is obligated
to honor them "somewhat."
I understand that you are concerned about not exposing yourself and your
family-to-be to the wrong kind of environment, but it is not as if she
is to blame. And you don't want her to think badly of Torah Judaism. If
you feel that home visits are too difficult, keep them to a minimum or
arrange for her to visit you. And you can still speak nicely to her over
the telephone. Anyway, when you move back to Israel, the geographical
distance itself will take care of most of this problem!
1. Interestingly, this ruling follows the opinion of
Rabbi Akiba, who himself was descended from converts.
2. Laws of Mamrim 5:11 and commentaries.