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Your letter was so poignant, do not give up the guitar! It is your passion and joy, why would you give that up just to appease family naysayers? All the better that pursuing it makes you slightly eccentric and I see no reason why you should not stubbornly continue to learn a musical instrument that gives you great pleasure even as you recognize that doing so is slightly absurd. Carve out time when you can; as others have said, even a few minutes a day, why not?
The author Alexander McCall Smith of the Number 1 Ladies' Detective Agency plays in an small orchestra of self-described terrible players, yes, people who enjoy playing their instrument of choice but are unable to do so very well. They hold a concert once I year, I think, just for the sheer ridiculousness of it. If you lived in Scotland, they would probably be delighted to have such a determined yet unaccomplished guitar player in their midst!
My own father took up piano lessons in his 50s and never did do very well at it but we adored him for it. He pounded out an easy version of the "Wabash Cannonball" for years and we thought he might just be stuck there but slowly he did improve and was able to play some nice pieces as time went on.
Taking up a new hobby is a positive example for your children (and your husband) - you are showing them that learning is a life-long process and that one should not be afraid of trying new things. Your guitar playing does not have to "go anywhere" for it to be justified.