The reference to a custody arrangement suggests that this is LW's husband's biological child, but that doesn't fit with the part about maybe not getting to spend time see the baby until she's a toddler.

If it is his biological child, it sounds like either husband cheated on his now-ex with LW, or vice versa, or a tight timeline in which the baby was conceived shortly before the official divorce, and he married the LW within the next few months. Neither of those possibilities suggests that the ex would want LW to be part of her life, or co-parenting her child in the way LW is talking about.

Legalities aside, going to court to ask for split custody would probably ruin the chances of a friendly co-parenting relationship.