Since I am a VA person here, hopefully I can help a bit with your situation.
Arranging custody while living in the same house, is not usually the norm, but I have seen odd things done in VA courts, so why not this one?
Now I will say it will depend on the Judge that you receive as most will say this is how it is done and then there are those very few that will try anything once.
I do really want you to think about it though in fullness.
Child is spending time with you in house, you decide it is bed time, Mom says no I want child to go to bed later, you say no I say now. You put child to bed Mom picks up child goes to her room, what would happen next? Would you just say ok Mom won that one or would it become a further arguement? UNDERSTAND?
In VA you MUST be seperated and living apart for 1 year and if the other party does not agree that you have done this, it can drag on and on. It is a question that when facing a Judge for divorce it is asked about 20 different ways, some are very subtle, so they can make sure you are following the guideline set.
Do not set yourself up for just a minium of overnights, as you have stated 2 nights and every other weekend. There are no direct guidelines in custody time in VA. I have seen from a few hours a week to 2 week periods to actual 6 months one parent with EOW and then 6 month other parent with EOW.
I will say VA prefers to appoint one person a custodial parent even with a 50/50 custody situation, that is due to school regulations. You must be considered the custodial parent for enrollment in school. They (schools) do not recognize legal guardians unless it is a child in need (a child who is in state custody situations)
You can receive, and most likely will receive joint legal custody, which gives you the rights to confer with other parent on all issues, from medical to schooling and in some cases religion, unless there is continuous conflict then a Judge may order that one parent be in charge of a particular area of conflict.
Joint physical custody, is normally what 50/50 custody is but as mentioned before, it normally has a primary custodial parent listed for school purposes.
Sole custody, is not the normal in VA, unless severe abuse situations, that are back up with court documentation is rare in VA. No Johnny/Mary hit me once and so I should receive custody situations.
Child care is normally split in costs, even if you have a free care provider for your time, you will most likely have to split whatever the costs are on Moms time.
VA is a joint income Commonwealth, so the courts look at both incomes when deciding child support. They will also place it with DCSEA (government agency to oversee that it is paid). Rarely will they go out of guidelines. They will though in cases order things like extra curricular paid in half, medical will be ordered in half with both parents required to carry some type of insurance. Transportation for driving child to and from each home can be done various ways, but most likely the parent who moves of of residental home will bear the costs.
Now onto another thing with transportation and it comes up often on this forum. Who picks up and drops of child. Most orders, state that the NCP (non custodial parent) will do both, unless it is specific that another responsible party may do the transportation. So when you actually do your paperwork think about that before hand and before you sign paperwork, because once it is set, it is difficult to change.
Taxes, ahhhhhhhhh lovely, lovely axes, a serious problem with most divorce couples ask Ldi. The normal in VA is custodial parent gets all the tax breaks, sometimes a Judge will order every other year with stipulations, such as child support being on time and paid for the year in full before Jan 1. So if you are behind even a dollar come Jan 1 of the next year, the parent who would not have gotten the tax credit, will now get that credit and if it goes to court, the Judge will have DCSEA pull records to show child support payments for the year, and if a dollar behind Judge will rule towards the parent that receives child support.
