Look, women almost always get primary custody because it is recognized that they are usually the primary caregivers for the child....so unless there is a reason to seek full-custody (your wife is somehow a danger to your child) then you shouldn't...because you'll lose most likely and you'll lose the goodwill of your wife most certainly.
women almost always get custody because society has decided mothers are the real parents. Even the best father is considered a poor substitute for even the worst mother. The only real way to counter this is to prove (if possible) that the mother is an active threat to the child's survival. As this is a sure way to damage a child, it really doesn't merit serious consideration (unless the mom really *IS* a clear & present danger, in which case, don't hold back). Sole-custody fathers have virtually no services available to them of any kind.
If you two are being quite amicable about this, then it would probably make sense to have a lawyer (who specializes in family law) help you draft a parenting plan. You NEED to get the joint custody agreement in a legally binding document.
quoted for truth.
This may sound bizarre, ridiculous, or whatever, but - if there are no lawyers involved, or if you have one lawyer assisting both of you (it may be illegal in your state for a single attorney to represent both of you in this), or you have a lawyer and your wife doesn't, the law will incline toward the view that your agreement is exactly how YOU want things, and so a court may consider itself compelled to act as de-facto advocate for your wife in any action down the road. The only way I found through this was to hire a lawyer to represent me, and hire a second lawyer to represent her (she chose the lawyer). This was, in part, to avoid getting royally reamed down the road, and also to establish a track record as a co-operative partner, should the future require it).
Nonetheless, you need to do some thinking. It's probably not in your daughter's interest to be shunted back and forth between two homes every other night. Your wife's home will probably become her primary home. This may not be what is best for you but it is probably what is best for your daughter. Spend some time thinking about her needs, your needs and your wife's needs, and get an agreement that balances them all. If an agreement is too lopsided, it will fall apart down the line.
Your daughter may come to call her mother's home her home, but don't assume that you're not fit to do the job yourself, or that her mom has some ineffable magic leg-up that makes her automatically a better parent: living without you may not help your girl in any way, so keep focused on her what you know about her, fight for what she needs, fight for your place in her life - don't let others take advantage of her - but don't expect a merit badge....
You're not alone, bro - as you've seen, many good men have walked this sad & sorry path; learn from it, let it clarify things for you, let it strengthen your resolve and give you compassion...not just for your wife, not just for your daughter, but compassion for yourself; there is no greater hurt than to lose a child, and anyone with a human heart will feel that loss, and to grieve it....
