Do I need onward travel proof for a 60-day visa exemption for my family flying from the UK to Thailand?

I just came from States last week @ Airport on arrival I got until 19th of November 32 days

You would get a 69 day visa exempt stamp in your passport. This is NOT a visa. Immigration staff can ask you for three proofs (proof of address, Proof of funds - 20.000 thb or equivalent in a major currency per person, and proof of travel out of Thailand within 60 days of your arrival date). But if you are a first time traveller to Thailand you are unlikely to be asked any questions by Immigration. However, many airlines will not allow you to board the aircraft unless you have a returm ticket. Best confirm the requirements with your airline

You get 60 days on arrrival no visa needed

I guess you mean a 60 days visa exemption. An onward ticket within 60 days is formally required for visa exemptions. Rarely checked at the immigration, but you might risk your airline will request it upon check in. You can alternatively call them and ask for their policy regarding this.

Your airline will be the ones that want to see onward tickets

There is no such thing as a 60 day visa at the airport. The only VISA you can get at the airport is the 15 day visa on arrival that you apply for and pay for at the airport and it's not available to those from the UK.

You are talking about visa exempt which is not a visa at all. It's you being exempt from needing a visa. Legally you are required to have proof on onward travel (a ticket out of Thailand within 60 days) but immigration only asks to see it rarely. It's your airline that is more likely to ask, and if they want to see it they won't let you board your flight without it. So ask your airline what their requirement is to travel to Thailand without a visa.