His family isn’t wealthy by all means. [not correct]
His family is by no means wealthy. [correct]
His family isn’t wealthy by any means. [correct]
The phrase "by all means" doesn't fit here. It usually means something like "certainly" or "definitely," especially in a suggestion or a command: "By all means, don't tell my parents!" / "By all means, bring your friends if they want to come!" (I believe it's roughly equivalent to 千萬, as in "千萬要來".)