Is she at the appropriate level for speech development? Stuffing food in their mouth is one of the symptoms that goes along with a certain kind of speech development delay. They stuff because their nerves are not able to tell them when their mouth is full and/or it takes a full mouth for them to feel the food.
My grandson who has speech apraxia did that. He had a very small vocabulary at 2 and he was and still is, at 4, unable to make certain sounds because his nerves and muscles are not developed to do so.
What I did with him when feeding him is to put just one mouthful on his plate at a time. When he swallowed that I added another one. All the time eating myself and helping his older sister stay focused on staying at the table and eating.
Sometimes, I fed the children before or after I had already eaten. Sometime I fed the children at different times. I still sometimes hand feed each child because they eat better when I do. I also think they associate hand feeding with the love they received as a baby when they had to be hand fed.
And then there's the sibling rivalry thing. In your case the other child has come into your daughter's space and she may see that as taking your attention away from her. If you hand feed one, siblings may want to do that too.