IANAL, but it's not that simple.
Section 3 creates the offence of unlawful interception and refers to Section 6 for the definition of "lawful authority". Section 3(2) doesn't apply as a parent cannot control the other party's use of the messaging service.
Section 6 specifies when a person has lawful authority. Warrants referenced in 6(1)(a) and 6(1)(c) do not apply here, so we fall back to 6(1)(b), which refers to Sections 44–52.
Of these, 44 refers to interception with consent; 45–48 refer to interception for business or enforcement purposes by the postal services, OFCOM, or businesses; 49–51 refer to interception in institutions such as prisons, immigration detention centres, and psychiatric hospitals; and 52 is in accordance with overseas requests.
Section 44 is the only one that reasonably applies and says that, except for an authorisation under Part 2 of RIPA where only one party need consent, both parties must consent to the interception.
In any case, Section 1 of the Computer Misuse Act would remain a sticky wicket if the sender withheld consent, and because the CMA is written so broadly (for better or worse), adding an exception to Section 1 where the legal guardian of a child has consented would cause more problems than it solved, especially if the intercepter for whatever reason turned rogue.
