The grounds alleged in a complaint isn't what's important - custody determinations are made on the basis of the best interest of the child.
Under the rules governing the conduct of attorneys in New York it may be necessary to remind you that this answer could be considered attorney advertising.
The court will award custody based upon the best interests of the child standard if the parties do not reach a settlement. The grounds upon which the divorce will be granted do not generally impact the custody determination unless there is a direct correlation with the custody issues.
Best interests of the child will be the determining factor. Not the basis for filing your divorce.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.