Ok I know you said no more replies but come on - one more k? :)
As a three year bereavement facilitator voluntarily at church I can't even imagine you wouldnt take her! Its up to you if she is quiet during the viewing or service then she stays if not backup plan and a car video is perfect. She can rejoin at the reception and yes see all the family. Children bring joy - funerals can be sad. Its important at two to begin to understand life and death. Seeing a dead body is not scary its not unhealthy its a part of life and a personal decision (yours not anyone elses). At that age she wouldnt get it anyway more than likely.
I just took my 13 month old to a service 5 hours away - we had a great time - it was good to see the family, they doted on him, he brought them joy during a sad time and during the service I was in the hallway most of the time while my husband (it was his uncle that passed) was in the service area. :)