Explaining a gap after caregiving or layoff (update)

I have been out of work for 3 months and worry about the gap. There are 3 people counting on me, so I am trying to be careful. I am nervous about being filtered out. What do you say in interviews?

I was hired after a 3-month gap. The manager said the skills test mattered more than the dates.

Keep everything in writing and save the confirmation numbers. It saved me later.