Hi thank you for your message, I appreciate this is important to you so I will endeavour to give you a quick but clear answer. Please note this is not a chat service so responses may not be instantaneous. If you are talking about recording your own children you do not need their consent. If you are recording your partner then you should obtain consent otherwise it is covert recording. There are a myriad of laws, regulations and guidance relating to covert recordings. There are legitimate reasons for some recordings to take place.
A recording may be unlawful (under the civil law) if it constitutes a misuse of private information, a breach of confidence, a breach of the GDPR or Data Protection Act 2018. One of the questions for the court is whether the individual had a reasonable expectation of privacy in the particular circumstances.
Consideration is then given to whether this potential breach of privacy is overridden by other factors. For example, journalists may have the benefit of data privacy exemptions or may claim legitimacy due to public interest arguments. It is more difficult for an individual to argue these sorts of reasons to justify covert recordings. In your case, it is likely that the need for a covert recording without your partners consent would not be justifiable and they could claim against you on that basis.
It should be noted that you have said you are only recording lessons but if you record other activity in particular, sexual activity without your partners consent then this could amount to the criminal offence of voyeurism.
Hopefully, I have answered your query in a way that is simple and easy to understand. If anything remains unclear, I will be more than happy to clarify it for you. In the meantime, thank you once again for using our services.