Having done many bank shifts on a ED ward, I'm utterly disturbed at the advice you have been given.
If your child is vegetarian, your child is vegetarian, no-one should be forcing them to eat meat.
5 fish fingers is not a normal portion size, the place I bank at would serve normal portions, we just serve pudding and lots of snacks. Once someone is not at risk of refeeding, 3500 calories a day sounds right. This is normally in the form of
3 weetabix, full fat milk, piece of fruit, fruit juice.
Crumpets with butter and jam. Tea with milk
Hot meal and hot pudding. Squash
Cheese and crackers, fruit. Tea with milk
Hot meal and pudding. Squash
2 slices of toast with butter and jam, fruit, milky drink
Penalties for not completing food - fortisips. 2 fortisips for every main meal missed, one for every pudding and snack missed. Fortisips are 300 calories each. 10 x 300 calories = 3000 calories a day. This would be increased by 500 calories if someone was exercising a lot.
Observations are for 1 hour from when someone finishes eating/drinks fortisips. If people do not complete meal within 30 minutes, they must drink the fortisips regardless of how much food they have managed to eat. This ensures people are not left looking at cold meat for 3 hours.
It sounds like your child may have been discharged prematurely if she is still unwilling to engage with eating?