Your question is should it be standard practice to have both parents sign the waiver, even if separated. The easiest response comes from a California maxim of jurisprudence, superfluidity does not vitiate. In other words, having both parents sign the waiver probably doesn't hurt. While it might be possible that having such a requirement could lead to litigation itself, (many single parents could view such a requirement as a form of discrimination, and in some states, a person teaching karate, and therefore engaged in comerce, is subject to certain nondiscrimination statutes), the reasonable application of a dual parent signing requirement is unlikely to get you in trouble. But, as I am sure you will hear from others, speaking to an attorney in your area about your concern is the only way to find an answer that reflects your state's law.
I wish you had more facts available concerning the incident that lead to the requirement. It is interesting that judo has been the source of much of the case law on martial arts liability. One of the key cases in California focuses on the duty an instructor owes ones students, and the trust students place in instructors. In one case, the pairing of a novice with a more experienced person, and the subsequent injury of the novice lead to liability.
While you should obviously address your concerns about a waiver to an attorney in your own state, in your discussions with counsel, also explore whether a written waiver is even helpful in injury litigation. In most places, a waiver will not protect you from negligence. At most, the waiver serves as some proof that the participant had been made aware of the inherent risks in studying a martial art (or for that matter any athletic endeavor -- try entering a fun run without signing a waiver). You should also discuss with your attorney what other things you might do to protect yourself from potential litigation. You might ask if it would be helpful to have a written student behavior policy governing the expectations of your school with regard to how one treats ones fellow students. You might also explore whether an indemnity provision in your student contract, indemnifying you in the event the student negligently injures another student, would be enforceable or helpful.
Good question Rick.