Just realized I never gave a serious answer to the topic.
That's a sad situation.
My niece is 6 years old, and she likes it when I come to visit, because I'll act like a kid and play games with her for fun, more than any of her other aunts or uncles. 2nd last time I visited, she launched herself at my ankle as I was trying to leave, holding my leg so I couldn't leave, saying "No, don't go!!!". The last time I visited, she had string, and she was tying my hands in knots that she learned from Girl Scouts, pretending they were handcuffs, so that I wouldn't be able to leave, and that I'd have to stay.
Just wanted to share.
Not sure what type she is in socionics, but it's definitely a heartbreaker.
In general, I would say 'yes', it is easier for children to become closer to their dual than adults - socionics is a somewhat flawed theory in that it doesn't incorporate the experiences people have that shape them. Certainly we are a combination of our genes and natural predispositions as well as our environment. In that way, if our natural predispositions in socionics are likely to be very compatible as duals, it would be more likely we could get along as children before experiences shape us in a way potentially unlike our natural predisposition.
That said, of course you need maturity as you grow to have healthy relationships. Growing as an adult can make having a relationship easier, if you're going in the right direction. Also, it's not like experiences should change you that drastically that you wouldn't be compatible, since you're fundamentally the same person at your core.
Also, it still shouldn't be relatively hard to find a dual with similar experiences once you start dating. If you've grown up in similar socioeconomic conditions, it's more likely you'd have similar expectations for life, family, etc.
And socionics only goes so far anyway, so there's no real need to worry. Dating is more about physical attraction and similarity on more levels than socionics, imho. Socionics is one aspect - an important one, but not everything.
It's likely your cousin's oldest child (2nd nephew???) likes you because you're an awesome person, more than just 'duality'. I would guess he'd eventually adjust after moving - it's good you got to spend lots of time with him while you could.
Do you visit him a lot? How is he doing now?