From the OP on the main blog it sounded like "Mark" just wasn't comfortable watching kids without help. If they are pregnant with their first, he might just not feel confident in his kid wrangling skills.
Regarding adults alone with children, I participate in a mentoring capacity for a high school club. One of the rules we had was that no adult (male or female) was to be alone with a kid. We could have two kids and one adult, or two adults and one kid etc, but until the 3rd member arrived, we had to sit with the security guard in the lobby. I saw it as a rule meant to protect all of us since the students and mentors may not know that much about one another. In the case where Mark is the husband/fiance's best friend, I don't think this should apply. Presumably, the character is already known.