I am going through a divorce and custody case that is not going through family court. Can people get served a sapena on a Sunday during my trial?

You can be served any time of day or night on any day of the week.
Depending on where you are at, for example while off duty I worked for a PI who did "legal service work" so I would come to your door on my off time and when I thought I could get you. If you are already in court, they can just walk up to you and serve you with a new service

Yep, 24/7 365 they just need to touch you with it.