Can you get an equity loan? I think that is your best shot--I'd be surprised if you could get a business loan for an office addition to a single family residence.

Unless you have a high income and little debt, you wouldn't be a good bet for most underwriters with two homes if they have two mortgages. Yes, a home equity might be your best bet, especially if your first home is already almost paid for. The better option would have been to explore a renovation loan thrown in with the mortgage. But, speaking from an expense viewpoint, a teardown would be much better than doing "more new construction than old". It's the integration of the new with the old where it gets to be expensive. And most of the time, that would be a cash build unless you can find the right banker.