Wow, R., expecting a year-and-a-half old child to sit for more than 15 or 20 minutes really is asking a lot. Expecting her to stay good-natured and cooperative for 45 minutes or longer is simply not realistic. And two hours of enforced sitting would feel like torment, emotionally and physically, even to most adults.
Consider that you want your daughter to associate mealtimes with happiness and family companionship, in addition to eating. At her age, she can scarcely understand the abstract and (to her) non-intuitive "oughts and shoulds" that grownups find so important. There is evidence that kids (particularly girls) who have too much control exerted by their parents are at a higher risk for developing anorexia in puberty or their teens, as a way to take back some control in one of the few ways available to them. Might be worth keeping in mind.
My grandboy, going on 3 1/2, is still a bit squirrelly when expected to stay in his chair for more than 10 or 15 minutes. This is completely normal for healthy little kids, who have very busy minds and bodies. He's a great human being, and is becoming more socialized by the week, without a lot of struggle and bad feeling. I'm not the least concerned that he will fail to learn table manners as he's developmentally ready. On my weekly visits, I am sometimes able to coax him to sit and eat a little longer than his parents, but it's probably simply be the novelty of a different person. Makes me wonder if your babysitter interacts with your daughter in a different way - you might want to observe how she does it.
Please enjoy your little girl's toddlerhood. It will be gone so soon, and you'll miss it. If you disagree with your mom's negative feedback, hold tight and go with your heart. I also recommend Love and Logic to help you train your child as she is ready, while still nurturing her spontaneous spirit and preserving family sanity. Blessings to you both.