I am going to write about the generation gap, as far as I am considcerned it is a very important topic especially for people who have children and for people who work with teens.

When I was younger, so much younger than today, I thought my parents didn't understand me because their lives had been very different of mine, m. My relationship was different, with friends, with couples; m. My way of thinking was different too... as a result my friends and I did a lot of things that we never ever we talked with grownupabout with adults.

I think the sentence is too long and have suggested breaking into separate sentences.
I don't understand the meaning of my relationship was different, with friends, with couples - perhaps you mean 'My relationships with friends and partners were different'
Only young children would say 'grownups' - teens would not use this term.
This seems like a formal piece of writing and the puntos suspensivos would not be used in this way; more likely a semicolon. In a text message... sure use the puntos suspensivos.

Now a adays, the scenario is different from those days, I am mother of three children and I think that I can understand them perfectly.

'from those days' not really incorrect but redundant and implied by nowadays (which is one word).

I realize that the society is different and the way of life is different too but despite all, I fell neargrew to be like them...

'I fell near them' I think you mean 'I grew to be more like them' but I am not sure.

When I was younger, so much younger than today, I thought my parents didn't understand me because their lives beenare very different ofrom mine, my relationship was different, with friends, with and couples; my way of thinking was different too... as a result, my friends and I did a lot of things that never ever we talked with grownups.