mama, I haven't seen the movie, but a friend/khevre of ours is in it (was interviewed) so I'm familiar with it. Have read about it as well.
The only thing I can say is that for me it's not an issue. I didn't have a bris for my boys because "my father did it and his father did it and his father did it ..." ... not in the least. I did it ONLY because G!d made an agreement with me each member of my family individually, and that was part of it.
If I wasn't Jewish, my sons and I wouldn't have that particular agreement with G!d and it wouldn't even be an issue. Not even a question.
I know you're got a mixed marriage situation thing going, but since you're not Jewish, and the child's Jewish heritage comes through the mother, then your child is not, by Jewish law, Jewish. And does not require a brit mila. Period.
Yes, I know that by the Reform movement Jewishness goes through the father with a nonJewish mother (within certain conditions), but that is even less of an argument to have a brit ... since the Reform movement doesn't hold with the sanctity of Jewish law ... so it's a contradiction to use "but we're Reform" as justification for insisting on upholding a "Jewish law" when it's not even a Jewish law to have a brit for the child of a nonJewish mother.
(I know that paragraph is kind of convoluted on first reading, but read it again, and it makes perfect sense.)