Irrelevant, the nature of your reason to refuse to work outside of scheduled hours is between you and your conscience. Be it a child, a dog, opera tickets, or Friday Night Magic - the rules have to be the same. Being a parent doesn't absolve you of responsibilities to patients nor does not being a parent increase your obligations to work additional hours.
Her disinterest in finding someone to cover is disappointing in a healthcare professional - but otherwise "I can't stay late tonight" is fine unless contractually you are on call.
This is potentially a reasonable point. If the surgeon can't make a compelling case to the on-call anesthetist that the case needs to be done, then the anesthetist present has a reasonable argument. That said, I've found that day shift staff may well stay late to handle a case they had already prepped for if that would prevent an up-prepped on-call from having to come in an hour later.
One of my parents is a physician and I didn't get to see them much when I was growing up (or even now); I intimately understand the point of view of those advocating for greater work-life balance in medicine. What I find lacking in the push for greater work-life balance is an acknowledgment that quality of care may be changing for the worse as a result.
What would you have had this person do? Leave their child unattended? Do you have children? Who takes care of them if you have to work late?