I'm a few years behind this thread, but you're the first person I've seen who spelled grandfather in Polish like I do...and it is spelled Dziadzi. For grandmother it is Babci (bab-chi). I grew up in Naugatuck, CT, but my Babci and Dziadzi were both born and raised in Scranton, PA. We think my Dziadzi's mother came to America from Galacia at the age of 16...around 1900. My Babci's family, at least her father, came from Mlawa between 1900-1910. I'm thinking that it may not be a question of where in Poland they came from, but a question of where they settled. The terms used for grandma and grandpa in Chicago I've heard of before, but in Scranton, it's Babci and Dziadzi. At least I know that Babci and Dziadzi are correct for grandma and grandpa since the Catholic nuns that run the nursing home where my Babci is currently living were ALL born and raised in Poland and they go back to Poland every couple of years to visit family. In terms of "Aunt" in Polish, I grew up calling my aunts "Cioci". But that is only because, they were brothers and sisters to my grandparents, my mother called them Cioci.
I look at the whole issue, especially here in the USA, is a matter of where you grew up or where your ancestors settled. Sort of like Coke or Pepsi---do you call it "soda" or do you call it "pop"...but be careful calling it soda in Boston or you'll get a glass of club soda. ;-) As Americans, we're a big melting pot and we make different languages our own. Take English...it's American English, not the Queen's English or Canadian English. Just like the "Spanish" speaking in Mexico, Puerto Rico, Texas, etc...is all different. In TX, it's "Tex-Mex"...a lot of slang.
And I'm just babbling on...sorry... Hope I was sort of helpful here...
Just a tidbit of Polish history: I live in San Antonio, Texas now and just Southeast of San Antonio is the oldest permanent Polish settlement in the US. Panna Maria, Texas. They arrived in Galveston, TX (100 families) in 1854 and WALKED to Panna Maria. Anyway, here's the article link: associatedcontent.com/article/2524213/homecoming_at_the_oldest_polish_ settlement.html
is it pronounced smoething like chochie (english)
Are you thinking of Cioci (that's how I grew up spelling it)...and I pronounce it like: Chu (like the "u" in hut) - chee.