Have you considered renting a two bedroom apartment in Great Neck? That may put you under $2800 and you get guaranteed access to elite schools. There are dozens of buildings within walking distance of the LIRR. The LIRR is only 25 minutes to Penn Station if you catch an express train - about $242 per month. 3 bedroom apartments are very rare (and expensive) everywhere.
I was going to suggest the same thing that Neil04 did....move to Nassau County. I live in South Nassau and take the Far Rockaway line to the city...takes 45 minutes ($242 for unlimited monthly). Western side of Nassau County is going to give you the shortest commute...but I know people in West Suffolk who get to the city in about an hour on the Babylon line.
I've also worked in some of the "higher needs" schools in Nassau...and compared to what I hear about NYC schools...you're kids are better off at a school in Nassau county.
barker and
Neil04, I live in Nassau right now and commute by LIRR. Further in than Great Neck, closer to Nassau/Suffolk border.
Although I haven't thought about moving to Great Neck, I agree that it would solve my school problem.
What it will not solve is my commute problem. My commute right now is 1h45m door to door. My office is half hour from Penn station, either walking or taking subway. Subway saves me only about 5 minutes because of transfers. However, when the weather is crappy I choose subway over walking almost 2 miles from Penn to office.
So commute will go from 1h45m to 1h25m and save me $34 off my monthly ticket. It will not reduce my subway fare. In addition, as the move will be due to divorce, I am concerned with my accessibility and availability for kids during the day if I have to come home quick for whatever reason. I won't have a spouse to help juggle these things. It will be all on me.
As for 2-bedrooms vs 3-bedrooms, I have to admit that I am at a loss here. I know 3-bedroom apartments are rare, but I seriously don't know how we will manage in 2-bedrooms as my kids don't share a room (please do not comment on this as it will not change and I don't need righteous comments here). So in a 2-bedroom place, I will have to camp out in the living room. As I commented above on this, I am fine with doing that temporary. However, it is not likely that I will move my kids again before they are done with High School. And sleeping in the living room for 5-8 years (older one will graduate HS in 5 yrs, younger in 8 yrs) is not going to be a good thing for any one of us. So I am really sort of stuck with the whole apartment thing.
I thought of renting a house, but I am not good with taking care of the house and utility costs a lot higher in the house then in the apartment. Plus snow clean up, lawn care, etc for which I don't have any time what so ever - see my commute time and add my somewhat insane work hours.
So yes, I am feeling stuck. Doing my research for now, but will need to start seriously looking starting in April.