Ehhh I don't blame oldest son. If when I was a teen my mother same to me with "You need to cancel your plans to watch your brother because it's an emergency! Oh me? I'm off to have lunch with your uncle to meet his gf" I'd have laughed at her face. She had a child, not the 17 year old. So it's her plans that need to get cancelled. If the toddler ends up with the dad at the hospital because her lunch plans were to precious, that's 100% on her.

If she had asked 17yo to babysit in advance it would be a different story. Or if she was also canceling her plans to join the husband at the hospital but needed an emergency sitter. But demanding your kid cancel his fun while you keep yours? Oh piss off.