From the original post, it follows that Lucinda wants to get to go home earlier than usual, and to do so with regularity. She shouldn't be allowed to do this unless she trades favors with the other student/employees on the service, after apologizing for implying that her time is more valuable because she chose to enrich her life by starting a family.
I worked full time through undergrad to pay for school, and there were many times that I wanted to leave work early to study. This is an example of a personal conflict between work & serious personal obligations. If my employer let me leave early (for school) it would be unfair unless others got to leave early, or I compensated the other employees for their (additional) work. My time studying has the same value to them that their time watching NASCAR and drinking has to me. The same is true of people with kids. My view is that properly caring for children is (arguably) the most important thing that someone does in life. However, I would rather you reorder your life so that the child is cared for, rather than you ask to leave a rotation early, if others can't too. My time spent with my lover and friends are as important to me as the child is to you. And even if it *wasn't*, The fact that you have kids shouldn't lead to you getting to have your rotation end earlier than anyone else, regardless of the (non-emergent) reason. So don't expect a sympathetic ear.
Parents are ubiquitious in our society, and most of the young parents I see tend to either reflect an attitude of entitlement to special considerations (because of the kids), or even open discourtesy to others. The degree to which this happens differs across individuals, yet I see it every day. You obviously care more about your kids than you do your co-workers time. Which, incendentally, is what we want parents--as parents--to be like. However, as a student/unpaid employee, I don't care about the personal obligations of others unless they are 1) emergent or 2) that person is my good friend. If a close family member dies, is hospitalized, or needs emergency care, you get to leave work early AND have a personal day. If you wish to be treated equally as a student/coworker, the parental considerations for leaving early vanish. We ALL want to go home. And I care more about my dogs than I do about your kids.
Don't ever ask someone to cover for you so you can leave early because of your kids, unless they are truly your good friend, and you should pray your fellows don't hear you asking the person in charge to leave for that reason. Otherwise, your implication that your time is more valuable than theirs WILL be guaranteed to offend.