Hi Sami and welcome to the forum.
I personally don’t think that it is helpful to take the fetters as precepts. These are insights which one has as a result of the practice towards stream entry.
If you know that you are not going to get enlightened/liberated/saved by praying with your family, but you do it out of compassion and love for them then this seems like something that increases wholesome qualities and doesn’t create more delusion.
Just keep doing good and cultivating your mind and you will naturally let go of any aspects of your life which you are doing ritualistically or selfishly.
Welcome to the D&D forum! We hope you enjoy the various resources, FAQs, and previous threads. We encourage you to use the search function for topics and keywords you are interested in.
We also ask you to please take a moment now to familiarize yourself with the forum guidelines: Forum Guidelines. May some of these resources be of assistance along the path.
If you have any questions or need further clarification regarding anything, feel free to contact the moderators by including @moderators in your post or a PM.
Third fetter does not merely capture the idea of adherence to rules and rituals. Only if they are accompanied by the wrong view one would be careful. For an example if the prayer confirms the wrong view of eternal soul/or a permanent existence of some form that would feed a wrong view as far as the Buddhism is concerned.
Your description looks like a different thing driven by the compassion towards your family.