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I would find out about going on the waiting list as well. Having an older sibling at the school would probably put your dd2 close to the top of the list if the school has sibling priority on its admission criteria.
An appeal for Y3 should be about why this is the right school for your daughter. Simply preferring to have both your daughters at the same school will not be enough. You will need to show that she will be disadvantaged if she remains at her current school. I would bring up the fact you have moved your older daughter and the reasons for that. You may be concerned that if she remains the bullies will pick on her. It would also help if you can come up with any features of your local school that are missing from your daughter's current school and would be of particular benefit to her.
Not an admissions expert (sure one will come along soon!) but as it's a place in Y3, there is no infant class size law to contend with, so your chances are much better. I know quite a few (well 3) people who have got places in Year 3 even though the year group was "full" on the basis the child had a sibling in school.
DD1 has just been successful in getting a place at our local school via appeal on the grounds of bullying at her current school. DD2 will still be at the current school but we would obviously prefer her to be at the same school as her sister. There are no places at the school in Y3 so we would have to appeal. Is this ever successful or is the sibling connection considered in the same way as distance from school, i.e. not at all?