I am not an authority and all I can tell you is my experience and what I have read and heard as a very involved public school parent for 6 years, but the law is that your zoned school MUST give you a spot. The only time they can reject you is if they are so over-crowded that they have reached the legal limits of students the school can hold.

I have never heard of a public elementary school not admitting their pre-K students into the K, even if they don't live in the zone. Once you are in, you are in and so are your siblings. In fact, even for Middle School, if you have gone to a District 2 elementary school, you can apply to District 2 Middle Schools, whether you live in District 2 or not. This may not be the "official" policy,, but this is the policy that is followed (although I have heard that the DOE would love to change this, but they are afraid of the parent backlash if they did. )