My mother knew I had an affair with GG. She drove us to the hospital when I had an abortion. She didn't approve, but she knew.
When our dynamic became a poly dynamic, I was open with her. She has been very understanding-even though she is very religious and very monogamous.
The key I think is in having self-confidence in your decision. Also, it helps A LOT if it's a joint conversation. It's REALLY hard to say "we have decided to do this unusual, commonly unheard of thing which looks like it may be cheating, but really isn't" if it's not WE having the conversation. You know?
The biggest suggestion I have for you would be to give her some links (if she's computer friendly) or print it yourself on the topic.
Lovingmore.com might be a good start. Also, I can't recall the link, but Redpepper (on here) might know if you pm her, there is a lady "kiki" who has been doing blog posts on poly with kids. I know she posted one by me and one by RP recently. You might ask RP for that link and give it to your mom too, since she's expressed concern about your daughter.
(fyi-if you want info about being out-feel free to pm me-we're out with pretty much everyone).
"Love As Thou Wilt"