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I’ve seen 6 year old kids do barre chords so I would agree that small hands are not necessarily an issue.
I struggled with barre chords until I started private lessons last month and he showed me that my form was wrong on both barre chords and scales. My thumb was too high up and my elbow as not pressed up against my side. As a result of both of these my knuckles were not parallel to the fretboard which limited my stretch and reach. As soon as I lowered my thumb n the back of the fretboard my reach improved. It also allowed me to get my index finger parallel to the fret for barre chords.
Two minor adjustments made all the difference. The other thing he taught me was to place my barre finger first which insures it’s up against the fret.
I still have a lot to practice to get quick at it but now see it is possible.
As for your arthritis that may limit you. You asked what to do, the answer is modify the chords to something you can accomplish. Play the mini-F instead of the barre F, play an open C chord as opposed to the barre C. Tony often shows alternatives to barre chords during lessons because he dislikes barre chords so perhaps look through some past lessons to see his modifications.