I have a family member who says this when she is not free. Always.
I always think it's said in a way as if they are better than us! Also, why the secrecy? Just say what you are doing!
I get it as an occasional turn of phrase when pushed for time but used regularly it's comes across really stuck up.
The type of person who is using this is always reluctant to do things with friends with her partner, often without partner but at weekends it's all about 'my little family' and meeting up with other families is a no-no.