Should I tell hiring committee about my interview opportunity at another institution?
Consider asking for an extension without giving a specific reason. People should expect that you are exploring options and that they have different expiration dates. Ask if it would be a problem if you can't make a decision prior to -date-. If they ask for more, say that you are exploring your options and expect to be ready by that date. But the details can remain private. Don't give the impression, however, that an offer would be unlikely to be accepted if another comes in. 

I can't predict, of course, whether you will get an extension. If you don't, then you need to deal with it as presented.

But assume that if they want to make you an offer then they actually want to hire you and not just fill a slot by some date. They have some incentive to deal with you, though they have other considerations as well.