I would tell him that he can post once weekly and all photos have to be agreed with you first
I am curious, would you be happy for a man controlling a woman's use of mobile phone and social media in this way??
This to me, is a red flag for potential domestic violence in a relationship. My therapist would agree too.
I agree that your husband needs to be present for meal times, and to be honest, I believe that phones should be off around children in general (I am a bit old school with this and accept that people don't agree). Saying that, my partner and I both have on call commitments which means that sometimes are "disconnect to reconnect schedules" simply can't happen, however, we do use the do not disturb function and set certain callers only (we do this with limited family members for Disconnect to reconnect times too.
I would speak to your DP, say that it you feel uncomfortable about it and suggest that there are certain times of the day, or week, where there's no mobile phone usage - perhaps inform him of the health benefits and ask whether he wants to be setting this example to his children?
I would also make the point of being involved in a weekly update if his family live abroad - it is harder to let grandparents feel included when they are a long way away and perhaps he is unconsciously over compensating for this fact; I am sure he wants his family to feel close to his children.
Do you skype / video call with his family? Perhaps offer to set this up weekly at a time that's suitable for you.
[By the way, I have contact with my parents daily and DP is the same; whatsapp, or a phone call, apart from the days we agree to not use mobile phones and computers]