Explaining a gap after caregiving or layoff - first time posting

I took time out to care for a family member after working as a bookkeeper. I would rather hear the honest version than the polite one. I am nervous about being filtered out. What do you say in interviews?

I listed the volunteering and course under the same dates and kept the explanation to a sentence in the cover letter.

I was hired after a 13-month gap. The manager said the skills test mattered more than the dates.