Could there be a porblem in a parent walking around the hous ein pyjamas?

Yes, there can be a problem with this, and it depends on the situation. Let me explain clearly. First, if you're walking around in pajamas in front of your children, especially as they get older, this creates a chinuch problem. Children learn from what they see at home more than from anywhere else. If a mother walks around the house in pajamas regularly, even if it's technically permitted when no strange men are present, the daughter sees this and thinks "Oh, in my mother's generation you wore pajamas inside, so in my generation I'll wear pajamas outside." The child doesn't understand the halachic distinctions - she just sees what Ima does and copies it. The poskim write that while there's no outright issur for a woman to wear pajama pants at home in front of her husband and children who are accustomed to seeing her this way, it's not proper from a tzniut perspective. It's better to wear a robe over the pajamas, especially when other family members are present. This is the proper and modest behavior. For a man, the same applies. You shouldn't walk around in your underwear or just in briefs in the middle of the house, especially if you have a wife and children. Even if it's not a biblical sin, it's not a good character trait. You're teaching your children bad habits. Right now you might be young, but one day you'll be older, and your kids will be used to seeing you this way. Do you want your son bringing his rabbi from yeshiva over and you're walking around in your underwear? You have to think about the chinuch you're giving.