You are referring to what the law calls vaicarious consent. The law on that is very mixed. There are two sets of laws that must be considered: the federal wiretap law and then the state wiretap law. Under federal case law, there is a limited ability for a parent to use vaicarious consent to escape prosecution for violating the federal wiretap laws for recording conversations between his child and others when the parent is not a party to the conversation. The 6th Circuit in Pollack v. Pollack, 154 F.3d 601 (1998) states the basic standard that seems to be the most used for federal vaicarious consent cases:
[W]e agree with the district court’s adoption of the doctrine, provided that a clear emphasis is put on the need for the “consenting” parent to demonstrate a good faith, objectively reasonable basis for believing such consent was necessary for the welfare of the child. Accordingly, we adopt the standard set forth by the district court in Thompson and hold that as long as the guardian has a good faith, objectively reasonable basis for believing that it is necessary and in the best interest of the child to consent on behalf of his or her minor child to the taping of telephone conversations, the guardian may vicariously consent on behalf of the child to the recording. See Thompson, 838 F.Supp. at 1544. Such vicarious consent will be exempt from liability under Title III, pursuant to the consent exception contained in 18 U.S.C. § 2511(2)(d).
We stress that while this doctrine should not be interpreted as permitting parents to tape any conversation involving their child simply by invoking the magic words: “I was doing it in his/her best interest,” there are situations, such as verbal, emotional, or sexual abuse by the other parent, that make such a doctrine necessary to protect the child from harm.
Note a couple of things about these cases. First, they only allow the taping when the parent or guardian “has a good faith, objectively reasonable basis for believing that it is necessary and in the best interest of the child.” The parent better have something good to point to as the basis for that belief, simply saying he thought it was necessary isn’t good enough. Second, these cases tend to only allow taping of conversations within the family or, in some cases, with a a nonfamily member who may be actually abusing the child.
But the problem here is that the proposed taping could well capture conversations that fall outside this doctrine, in which case the OP would be exposed to possible criminal prosecution under federal law. Moreover, the OP would be unable to use any such illegally obtained recording in court.
Not all states have addressed the issue of how vaicarious consent will apply under the state wiretap laws and those that have have arrived at different rules for it. Some states reject it altogether.
The video part of a recording raises different issues, and again the lack of control over what is being taped will be a problem.
Thus, before attempting any such taping, I would strongly urge the OP to get very good legal advice from a criminal defense lawyer in his state. The consequences if he gets it wrong could be quite severe.