There are a few feeding systems where the nipples of the bottle can be used as an insert in the cup. The cup generally has handles on each side to assist child with holding. I would be using something like that at the table for the child with you holding the child's hands on the handles. Then as she gets it try swapping out the nipple for the sippy spout.

As for the fruits and veggies it isn't your job to serve something other than what you are serving to others her age. Mom can make up the difference at home at breakfast and supper till she teaches child to eat what you are serving. I have one in the same situation who is closing in on 17 months and mom still gives the little motts cups for most of her meals at home and other than sometimes a piece of banana eats no fruit at my house and been off veggies since 15 months. She gets a bit of pasta on her plate and 2-3 pieces of the fruit or veggie as I know I am going to waste it and the hope is that she will eat it some day and like them. Her mom still warms her bottles for her morning and night but says I don't have to. As a result I manage to get 3-4 ounces of milk into her the whole time she is with me but as long as I hold my ground she will come to realize there is no other choice.