Wow sounds so similar to what happened to me, ex was cheating on his dp with me.
Told me he lived with his DM who didnt approve of me having DC (reason I couldn't go to his house)
Had to be home by a certain time (time she got home from work)
Had to spend 'quality time unninterrupted' with his dm on a sunday (his and his dp would visit her parents for lunch).
Always started an argument on birthdays, xmas and valentines day (obviously he needed to show face at home)
He skyped me at home but always made excuses why he wouldn't show me around his house, or his bedroom (obviously photos and her stuff etc)
He always seemed to answer his phone in the bathroom and only after it rung for ages (clearly had to sneak away and hide to take the call. Except during the hours she was at work. She worked different hours to him)
We lived close by to each other and a few times I caught him out and about when he said he was at home busy (always had a plausible excuse involving some type of lovely surprise for me).
3 years this went on, it got to the point I stuck around just to find out the truth, but for a very long time he kept me dangling because everything he said did sound plausible.
Btw, the person telling him to keep it down while you he was skyping you at home could very well have been his dp. He could've told her it's a business/ work call. Might explain why she never entered into the room. Maybe she was trying to get their baby to sleep 