What does “soapbox-ready” mean?

Literally, a soapbox is just a (usually wooden) packing case for soap. But from Merriam-Webster

soapbox: an improvised platform used by a self-appointed, spontaneous, or informal orator; broadly, something that provides an outlet for delivering opinions

Here are some written instances of "[get on a] soapbox about it". As often as not people use it in the negative ("I don't want to get on a soapbox about it" means "I don't want to make a big speech"). It's a fairly common figurative expression on both sides of the Atlantic.

The fact that the definition mentions an improvised platform doesn't always imply that the person delivering their opinions has only just thought of whatever they're saying. There are people who go to Speakers' Corner in Hyde Park London, year after year, delivering the same rants. Obviously they gradually refine their words based on how much support they get for different versions. But even a person who's never spoken there before would probably spend some time working out how best to put across what he wants to say.

So if this woman's vocal anger towards her sons sounded "soapbox-ready", it means she seemed to have her words carefully planned in advance, in order to have the most effect. Which is unusual, since normally when people erupt in anger their words are spontaneous, not prepared.

As noted in previous answer, a speech being "soapbox-ready" means it's ready to deliver. While the Soapbox article in wikipedia refers several times to impromptu speeches, it also mentions a number of cases where speeches are given repeatedly. Use of the term in the review is intended to add interest and color, even if the metaphor is imperfect.

In the other two instances mentioned in the question, one ("Town Crier getting his bell and Soapbox ready") refers to the most-usual sense, speaking or haranguing in public; the other refers to small unpowered race-cars, as illustrated in wikipedia's Soap Box Derby article. Some 1930's entries were made from wooden orange crates and presumably from wooden soap boxes as well. The Delcam vehicle is mostly of carbon-fibre construction.

Someone hereinabove explained that a "soapbox" is a box of soaps for shipping and it was built out of wood. It's right, apart from the meaning: imagine yourself in the past as someone wanting to make a speech before the public; they stood up onto a wooden soapbox to make themselves visible. This the source of soapbox meaning.