Are Soldiers authorized absence to care for a child while civilian spouse works?

Is this one of those, “I’ll pose a question for the group” type of questions, or are you actually asking for yourself?
Respectfully, you’re a Senior NCO. You ARE the leadership. You should know the answer to this.

Frankly, leadership can do just about anything they want, so long as it’s not illegal. “Wallace, don’t you have an off post appointment all day tomorrow? *foot stomp*. Don’t worry about PT formation, just call in at 0800 to let us know you’re alive.”

Do they have to, no. Can they, of course. It’s not a big secret how joes rack up 50, 60, 70+ days of leave. And it’s not because they’re deployed and not taking days off.

As long as leadership is not allowing anything illegal, immoral, or unethical... they can allow whatever they want. The trick is getting the leadership to want what you want allowed.

It's the discrepancy of the chain of command but don't be surprised leaders sits down with the Soldier to discuss a long term plan because that may not be acceptable long term depending on the unit's mission and schedule.