Yes, it is possible that the fact that you allow notifications from the relative in the group text is why you kept hearing the pings. When you have Sleep Focus enabled, notifications from your allowed contacts are still allowed to come through.This is why you heard the pings from the group text, even though Sleep Focus was enabled.
If you want to avoid being disturbed by group texts when you have Sleep Focus enabled, you can either mute the group chat or remove the relative from your list of allowed contacts. To mute the group chat, open the chat and tap the group name at the top of the screen. Then, tap the "More" button (three dots) and select "Mute notifications." To remove the relative from your list of allowed contacts, go to Settings > Focus > Sleep Focus > People and tap the "Remove" button next to their name.
Dominik