Vertaling - Pools-Engels - Cześć wujek! Dzisiaj są Twoje urodziny.. Życzę...

Only thing, that comes to my mind is swapping "I whish you all the best" with "Best wishes" but it may actually be wrong in this form...

Hi Hazok,
The translation must start from "I wish you...", because there are more things that follow "all the best". "Best wishes" are being said as a separate expression. See what I mean?

I feel that word "joy" should be replaced by "consolation" in the translation.

Hi durklis,
Im' afraid "consolation" is sth a little bit different than "pociecha z dzieci".

Look at the example:
"After her husband's death, she found great consolation in her children".

We can get consolation/comfort in children after sth bad happens to us. Meanwhile "pociecha z dzieci" means moments of joyfulness and pride in our children. But indeeed I was thinking very hard how to express it in English.