Their being a "family owned business" has nothing to do with anything, and I can see how that would strike you as a dumb reason to justify an action or an inaction.

Their corporate structure or lack thereof is irrelevant.

All that matters is the language in the parties' contract, which shows the parties' intent. That, and the facts of what the parties have done or not done (besides asserting this dumb family-owned business claim) is what a judge would look at in evaluating any complaint's allegations.

If the parties' contract agreed on your money's non-refundability, expect a judge to enforce that, unless your contract says that a force majeure event entitles you to a refund.

That's a great question. We're unfortunately going to see a lot more questions about this topic the coming months. So, let's bat this around generally just a bit:
(1) If the amount is small, you can take them to small claims court. No lawyers there but you'll need to read the contract carefully to understand your arguments. For these questions coming up with coronavirus cancellations that aren't a lot of money, the person who holds the money has the upper hand, whether the person wanting to keep a deposit or get it back by way of example, unless the other party is willing to invest the effort in small claims court.
(2) If it's enough money to warrant getting legal counsel involved, and assuming there is a written contract (and there should be if its more money involved), the terms of the contract control. The attorney will need to review those terms and how they interact to give you an answer. The facts of your situation and how well the contract was drafted will make that answer more or less clear regarding your likelihood of prevailing. In some circumstances there might be other claims besides breach of contract involved. That's where the lawyer is worth paying!
(3) Economics always matter in litigation. The worst thing in the world is paying the lawyer and then feeling like you didn't reach your goal. The first thing I always ask a client is what their goal is. Examples: Do continuing good relationships matter? Do you have the money to take it all the way to trial or do I push hard on early settlement compromises? Also, if you have a written contract (in California) and it doesn't provide for recovery of attorney fees, you don't get to claim them in your recovery. You would have to have another claim to have a shot of getting your legal fees back. Many people don't understand that and think that the winning side always gets their attorney fees back. Those types of considerations are important in understanding the economics of your case and formulating the best approach for the client.
The economics are saddening on BOTH sides with the covid-19 coronavirus and, unfortunately, courts may have to step in to determine where the hardships fall. Mediation and arbitration are also often lower costs options.

It’s early days, yet—but a company trying to survive this is more at risk of complete failure them an individual,. We’re all in this together. You may want to remember that.

We can’t speculate on a contract we have not read and as indicated above unless this was some expensive event it’s not economically sensible to involve attorneys to review the contract and details. Try a credit card dispute or small claims court.

A great deal will involved on the terms and conditions of the sale. This would be a small claims case so the legal fees will be close to $0. Best wishes.