Yes, I think you're trying to cover too many places. Poland is a huge country. But exactly how many nights will you have in Poland?
I'd start by scratching Sopot. Unfortunately, I don't think that's enough--though of course it depends on what you want to see and do, plus I am looking at things from the perspective of an adult who spends a lot of time in museums. My 2018 trip also had a heavy focus on Cold War sites, because that's a special interest of mine. Poland has done an exceptionally good job of making its key historical sites and its museums English-accessible. As a result, you're not typically spending just 30 or 60 minutes somewhere. There's a lot of very good information posted in English, and it takes time to read it (or watch videos). I spent 20 hours (!) in Gdansk's WWII Museum and 8 hours at the Solidarity Center. POLIN (Museum of the Jews in Poland) and the Warsaw Rising Museum took me about 8 hours each.
I don't know how appropriate Auschwitz is for a 9-year-old, but getting to the camp and visiting it takes the better part of a day. The Schindler Factory takes probably at least 2 hours (over 4 for me, I think). And Krakow is gorgeous, so you want to have time to enjoy the city, Wawel Castle, etc.
Let's see what folks who actually have children (I don't) think about you timing.
As for transportation within Poland:
Warsaw - Gdansk is under 3 hours by train.
Warswa - Krakow is 2 hr. 20 min. by train.
Gdansk - Sopot is 15-20 minutes by train.
Ergo, trains are the way to go.
If you have Polish ancestry, you might be interested in the Emigration Museum in Gdynia (also near Gdansk). It's modern and full of English. I wouldn't particularly recommend it on a very short trip like this if you're not Polish, though the emigrant experience is pretty universal.