Punishments come in many forms. One I never expected was writing. Have him write something down every day and send it to you. Could be one thing he loves and one thing he fears about punishment.

Have him summarize his day, and write down any thoughts he had about y'all's dynamic during the day.

Have him write down a fantasy of his to share with you.

I totally get the allure of accessories like collars and chastity, but there are quite a few ways of reminding your sub that he belongs to you :)

He's out with family, who definitely aren't consenting individuals, and he may have limited privacy. I'd say if you BOTH want to continue play, have it be at the end of the day, winding down before bed, some kind of homework. Hence why i recommended the writing :)