Child Custody mediations are usually either set several weeks in advance or are done on an emergency basis (sometimes called a screening). You may certainly request a continuance. Based on your question, you are asking for a continuance of one or two days.
I don't practice in Riverside County. However, Chapter 5 of their local rules (available online) is the Family Law Section. You should review the rules, starting at 5.0055.
You should also ask the other parent (unless a restraining order prevents contact) if a continuance of a couple days is agreeable. If so, contact Family Court Services in Riverside County (address is on the notice you received) and reschedule.
Riverside may have a Stipulation and Order form in their Self-Help Center for this short continuance.
I suspect that child development experts would say that a couple days to a six week old makes no difference at all! It's hard to imagine an objection to a brief continuance.
An emergency mediation is one set by the court because a party has submitted an "ex parte" or one-sided emergency request to change the custody of a child. It can be scheduled with as little as one business day's notice. The court will not consider your mid-term cause to reschedule and if you do not attend drastic changes could occur with the custody of your child. You need to let the professor know about the court hearing and go to the hearing, you should be allowed to re-take the test. If you can afford one, you should seek out an attorney in Riverside who can help you with this case. If not see the family law facilitator at the family law assistance center in the family court in Riverside.