My son is 2 1/2 and hasn't taken a bottle in over a year. On the other hand, my friend's daughter will be 3 at the end of the month, and she still takes one every day. It has not delayed her speach AT ALL. This child was CLEARLY speaking in full sentences at 14 months. When my son turned 14 months and would give me 2 word senteces, I thought he was behind because I was so used to how well she spoke.
That said, if you don't want the bottle anymore, get rid of them. I know it's hard to stand up for yourself against a parent. After all, we used to get told we were "sassing" and got in trouble for it. You need to tank her for her input, then remind her that you're a mom now too. If you're Christian, you can remind her that you are trying to teach her to "Honor her Mother and Father" and that her contradicting your authority is teaching her that she only has to obey WHEN Mom's present. BTW, if she tries to tell you to "honor her" by letting the baby keep the bottle- Gen 2:24 "For this reason a man shall leave his father and his mother, and shall cleave to his wife; and they shall be one flesh." Remind her that you are under your HUSBANDS authority and guidance now. That you will always respect her, but you now need to be able to help lead your own family.
A women's mother has a way of making you feel guilty for being a great Mom. I'm not sure why they seem to be this way, they just do. I think in someways some feel like their time is running out, and every time YOUR baby crosses a new mile stone, they get a little closer to their grave. Maybe you can find a silly song or special book that is JUST for your Mom to share with her. Something that can last as long as your Mom does. She may just be viewing the bottle as her special "Grandma Time", so finding a new version may give her something else to cling too.
I hope it goes well with your Mom! ~J.