Will this work? 

My soon to be ex and I had a long conversation the other day and we may have come to an agreement. I'm quite ignorant with these things so I'm not sure if this is a good idea or not.She was really mad at me until I convinced her that I do not want to screw her over. I want to work with her so it can be as fair as possible. Another consideration is the children. I want to disrupt them as little as possible. The idea we came up with is to basically share the house until the kids graduate from high school which will be in 3 years. When I say share, I mean we will alternate living here two weeks at a time. On the weeks we aren't here the other person will stay in a one bedroom apartment that we would also share. The reason I think this is the best plan comes down to money. IF we take the traditional rout and both of us hire lawyers, we will spend a fortune on that alone. I figure $7000 at least between the two of us. We will have to sell the house and then both of us would have to get a 3 bedroom apartment. This would cost more than our house payment and a one bedroom apartment. Another factor we are thinking about is that the housing market is down. If we can hold on to the house longer maybe the market will come back and we can have a bit more equity when we sell. I would also have to pay maintenance and child support so when I add this up in my head it makes sense to me. It would also be nice for the kids to stay put and not have to move.
The pitfalls I can see are:
If one of our situations change (Like either her or I find someone to be in a relationship with) it could get awkward.
Phone calls from boy friends/girl friends.
Seeing a girlfriend or boyfriend at the house. 
One person leaving things a mess for the other one to clean up when they arrive.
Disagreements or hurt feelings leading to games involving the house or apartment.

I don't know if I've hit all the pros and cons but I'm seriously considering this option mainly due to our financial situation. If we do this I have to figure out how to proceed. Do we still have to get a lawyer for all of the legal paperwork and proceedings? Is this even possible?