I've heard, but do check, that the biggest factor in custody is who usually takes care of them. Likely, she'd have to pay child support to you.
But is this a thing that needs to fill your time? I admit to doing the same, and knowing both options is healthy. But...you've said saving your marriage was your #1 concern - so I think you should focus there unless you change your mind (and you are sure - ignore the angry moments)