My situation might be slightly different from the question Should I tell other interviewers where else I've interviewed?.
I have received an offer from my home institution (institution A), and the deadline for a response is fast approaching. I also received an interview request for a similar position from institution B, whose hiring decision may not be available before the deadline of the offer from A. Personally, I am more attracted to the position at institution B. Should I tell the hiring committee at my home institution about this interview at institution B to get an extended deadline for the offer from A?
One potential complication is that one of the committee members at my home institution provided a recommendation letter for me. My inclination would be to be upfront and honest, but my family have different opinions.