The Lucy Show was quite good the first couple years when Vivian Vance was a regular -- the two had some wonderful chemistry. It lost a lot of spark when she tired of the grind and became just an occasional guest star. Here's Lucy never really clicked for me. The show was too over the top (I Love Lucy, even at it's most outlandish, was still grounded in believability and reality), the characterization of Lucy Carter varied wildly from show to show, there was little to no continuity or consistency of overall backstory or premise, and the "celebrity of the week" stunt casting became irritating and smacked of desperation. Gale Gordon, who was wonderful as Mr. Mooney, by this time had become a caricature of himself as Uncle Harry, with lots of bombast and little substance. The show still had some good moments here and there, but even Lucy with all her talent was unable to overcome the poor writing, and as time went on she became more and more involved in running things behind the scenes and less and less focused on acting (through much of the Here's Lucy run, she was relying on cue cards for her lines).
As for her kids, I actually thought both Lucie and Desi, Jr. had some considerable talent at their young ages, and Lucie especially seemed destined for a solid career in light comedy. I'm surprised she never really had consistent success after the demise of Here's Lucy.