Stick to hugging the girls only and small kids (7-8 max age). The reasoning is that they really are na-mahram, and the thinking of your father's family probably goes that if you think it's ok to hug your cousins, then you think it's OK to hug other guys.
I honestly never understood the mehram/na-mehram thing. If you are pure of heart, then what's the big deal?
Please don't justify why a wrongdoing according to the the Qur'an is OK. Just because you don't understand it and you think your "intentions are pure" doesn't make it right. If you think it's socially acceptable, that is up to you to decide, but strictly speaking it is not religiously acceptable and not right in islam.
Eg. Wearing perfume for women is not allowed in Islam, but say someone felt like they sweated a lot and need some to cover it, so they put it on. Their intentions would be "pure" because it wasn't meant to attract someone, but as they pass a man, he smells it and turns around and looks to where the smell is coming from, he sees her and his gaze lingers on her a bit as he studies her. Pure intention = not pure outcome.