Whether you file or not, you should talk to lawyer. If all of your actions are motivated by child related fears, the lawyer can advise you on what to do to make sure you have access to kid and look good during potential divorce. Marriage counseling might be a good idea too. The relationship has zero chance to rebuild if both of you don't change. (She for obvious reasons and you basically so that you wont become victim of the same thing again. It sounds like the more you try, the less does she, then you try more, then she does even less. That is bad dynamic.)

If you by the end of your home work have to ask how was the day and then are surprised over those Facebook details, then there is not much difference against being at work from the relationship standpoint. I don't mean it as blame you, just that this would factor in into relationship social network present or not.

But you know, that does not explain polygamy part still. Not your fear of child being used against you.