I think what you’re actually asking is a different question altogether.
You need to develop confidence so that you won’t feel inferior to others. It can be really hard to get over it if you have been bullied or made fun of when you were younger, but it can be done.
You want to fit in, and you want your children to feel comfortable and accepted by their peers. Nothing wrong with that.
But,
Aping other people’s clothing will only get you so far. As you have said, there are cues through which others can tell that you are from a different background. Humans are programmed to recognise when people are not exactly like us, we do it instinctively.
There is nothing wrong with being a little different. You don’t need to be exactly like them. You need to find those people who don’t care, who are decent enough to look past differences in background and/or ethnicity or whatever, and fall in with them.
Mostly, you need to develop your sense of entitlement. You are no worse than them, and they are no better than you.
I’m afraid that on the clothing question we probably can’t actually help you - the styles and brands will be specific to that area.