HP, it appears to me that 2houses will synch with your Google calendar, plus has features such as change requests, expense trackers, and some other things specific to shared parenting. My thought is, it you can synch with Google Calendar so that it doesn't require much extra effort on your behalf, then it might be a good thing. I especially noticed the feature where change requests are automated and you don't have to talk to W. Might work for you.
All five of us keep a shared Cozi calendar. My H also keeps a separate Outlook calendar. You could keep Google Calendar for your work/personal stuff, use 2houses for kid stuff. Just a thought.