I found 'neutral territory' helpful. My child is a teen and I found a
neutral environment helpful.
Preparing the children in advance
can also help - i.e. "Lets go bowling on Saturday. Do you mind if I bring
my new friend along?" sort of thing (explaining as much or as little as you
are comfortable with).
In my experience I wouldn't have the
'meeting' in your home. My mother brought her new boyfriend (who became my
step-father) in to the house for the initial meeting and I felt threatened
(I was 6)
All the best