I've been to about 15 births now, and I've seen home birth, birth center birth, and numerous hospital births. Every woman has her her husband with her, though they have provided varying degrees of support. I'd say only about 4 of these women had their mother in the room with them the whole time as an additional support person. And by the whole time, I don't necessarily mean during pushing... Sometimes the mom has left for that part. I just mean for what felt like virtually the entire labor.
The first time I doula-ed with the grandma-to-be, I thought, "I definitely would not want this woman in the room if she was my mother." It's not that she was terrible or annoying, but when she gave birth things were so different. Many grandmothers are thinking of their own birth, which was more often than not in a totally different time. They say things like, "doesn't everyone need an episiotomy?" and tell stories of how it was in her day, and sometimes make the laboring mamas very annoyed.
Some grandmothers-to-be benefit from having a doula present, for the same reasons that the dad or mom do; the doula is a less subjective person who is trained in all aspects of childbirth and can provide unique informational, emotional, and physical support. At times it is hard to be a loved one and watch objectively as your daughter or your wife seems to "suffer." Grandmas that might be simply too subjective may not be able to provide appropriate support to the laboring woman.
Sometimes grandmas are great! I had a recent birth where I just adored the grandmother-to-be. She was so chill and laid back! And of course, always a bonus, she agreed with me about how what the nurse said was weird, how a certain recommendation seemed totally unnecessary, etc. I thought she was a perfect support person - calm, quiet, provided pressure when needed, went and got cups of ice water and food for the mama, kept superfluous family members out, etc.
If my mother was like this woman, I might consider having her at my birth. As it stands at the moment, I don't think my mom would be the calming presence I'd want at my birth. Not that I don't think she'd be helpful... I think she'd think of ways to take care of me. And her birth was actually quite intervention-free and she supports my doula work, so she is knowledgeable of natural birth. I just don't think I would find her a soothing presence in assisting me to go into a relaxed inner birthing state, since I am naturally more stressed around her.
What about you? Would you want your mother in the room with you? Or anyone else?