Quoting Michelle Culliford:" So I am being induced on Friday and its been really troubling me on who I should allow in the room when ... [snip!] ... that she should be there to see her grandchild come into the world and I don't want to hurt her feelings. Need some advice???"
Tell her the truth - you love her and don't want to hurt her feelings but you need privacy.
Personally I wouldn't be cool with giving birth in front of my mother either. You shouldn't have an audience. You should only have people who will support you and sort of cheer you on and make you feel great about everything. Especially with an induction - the smallest thing that makes you lose your focus can stall your labor. And if you're just worrying about your mom stressing, then that's not going to help move things along if you KWIM.