Was Stalin's family wealthy

No, Stalin was not wealthy, but he did not have to be, because all of the resources of the Soviet Union were available to him for his living conditions. Stalin did not need to accumulate wealth and he didn't. He was paid on salary like every other person who worked for the government. At the time of his death unopened pay packets found. This was not because he was wealthy and did not need the money. It was because the state provided everything he needed.