KindergartenKop cul is not an insult, it means ass and so you would say - I wouldn't but wouldn't be shocked to hear it in a shop - ce jeans te fait un beau cul. Or you want to sit down on a sofa, and there is no space, so bouge ton cul.
Personally I don't like cul, and I never use it. However culot (the nerve, the cheek ) and to a lesser measure culotté are absolutely fine in most context. Quel culot is quite a nice expression actually.
Babyinmytummy no, not on front of babies, especially not my babies. Merde and putain are mostly muttered to myself than said to someone, like just finding a parking spot at the beach and realise I have forgotten the bag with the towels at home (we are in Australia) .
I wouldn't say chiant at work, but it wouldn't be unusual to say je suis dans la merde, j'ai besoin d'aide or when talking about someone to say c'est un emmerdeur .
there isn't a define line. It is subtle. The person you are talking to and the degree of intimacy is really important. And the same word has many meaning. If you ask me about the latest movie, c'était comment ton film hier soir? and I reply c'état hyper chiant, on est sorti avant la fin.
Somehow kids know that they can say some words but not others. I always tell my kids (all teenagers and all taller than me including the DDs) off, you can't swear until you have a university degree, but the same word , for example bordel, can be fine. So I don't say, bordel arrête de taper sur ta soeur, but would absolutely say to DS range moi ce bordel, tu devrais avoid honte de ta chambre. As it can mean mess or a massive problem, quel bordel, qu'est ce qu'on va faire .
To solve your situation. Just say to your DH that you understand that his family is quite relaxed when it comes to using everyday words, but that he should understand that to a British ear, it makes you uncomfortable and that maybe they can reduce the amount of merde, putain, fait chier, around you and the baby. You can't say much about bouffer if this is what they use instead of manger.
You learn a language you learn a culture, and the relationship with les gros mots is part of it. And it is evolving with the introduction of verlan. I am too old to use verlan, but my kids or their French friends will say chelou, truc de ouf, teuf..... but because it is something I hear it in movie or the music my kids listen to, but I didn't experience growing up, I don't use it.
Maybe start talking verlan or straight argot to shock your DH 
. Say c'est l'heure d'aller au pieu, je me casse, je vais dire bonne nuit à ta reum