I don't really know the answer OP as I haven't ever done a share, but here's my guess.
Both families are employers in a share situation, so both families need to be paying taxes, having an employer ID number, etc... It doesn't seem likely (or even wise) that you could somehow skirt this under one account set-up.
Also, perhaps you have dependent care FSA plans you can use? If so, you'll need to be able to demonstrate that you paid for childcare.