I don't think this is about discipline.
An hour & 45 minutes? I have a 2 year old (just barely) and there is no way I would expect her KNOW that there is a time & place to be quiet for an hour & 45 minutes. There attention span, at most, is 15 to 30 minutes.
You need to bring LOTS of things for her to do. Coloring books, paper, crayons, favorite toys, and books. Snacks & drinks.
Is there music during the services? Is it upbeat? Encourage her to get up & "dance" during those few minutes to help burn some energy off.
Even with all of that, I would still expect to have to take my DD outside or in another room to run for a few minutes. She is very high energy, always running or moving, and very curious about other people. I just can't imagine expecting my DD to be quiet for almost 2 hours without bringing something to occupy her.