We are a retired couple (75 & 70) who want to do a house swap in the US for tourism purposes of just under six months (it will be registered with Homeexchange.com). Can we enter on a VWP, stay for three months, have a two-week trip to South America, and then come back to our home swap for another 90 days before returning to Australia? Or do we have to apply for a six-month B1/B2 visa - and can we get one for this purpose?
I'd recommend applying for a visa, so you can explain the intended purpose of your visit. You say that you intend to enter the U.S. for three months, then leave for two weeks, and then return again for another three months. While this is technically legal under the Visa Waiver Program, this will raise some eyebrows from immigration officials the second time you enter, as they may believe that you're trying to keep residence in the U.S. by leaving on short stays.
When applying for a visa, you can explain in advance to consular officers the intended purpose of your two visits to the U.S., so that they can issue your visa on that basis. Likely, if they decide to issue you a visa, they will issue you a visa that allows for multiple entries, so you'll have a much easier time at U.S. immigration.