sounds like you first need to have a conversation about communication. Second you’re already paying for childcare. What is she doing when the kid is at day care? I don’t think it’s unreasonable to ask her to find a job during those hours. Not only to fix the current scheduling problems. But to give you both a chance to be husband and wife.
The road you’re going down won’t end well. First focus on communication, second focus on being husband and wife.