Hello -
I'm no expert at all, but I read your situation and I'm really interested to see how this would pan out for you.
Not sure what your wife's employment background is, but could she go to the UK and work for a different employer in the UK to meet the financial requirements and then sponsor you? I know there are two different categories for that route - one that applies to employment for less than 6 months, and one that applies to more than 6 months. You could go over for up to 6 months as a general visitor while she does this. Your children would be able to go over anyway because of your wife.
Or, maybe she could register the business with HMRC in the UK and operate within an equity partnership? I just learned from another poster on here (who is much more well-versed than myself) that an equity partner in a business partnership who draws salary from the profits of the company will be able to apply under the salaried employment category. It says that here (from the Annex FM 1.7):
9.5. Self-Employment as a sole trader, a partner or in a franchise - Requirements
9.5.2. Appendix FM-SE further specifies the requirements for self-employment income:

9.5.1. A sole trader is a business that is owned and controlled by one person, although they may employ additional staff. A partnership is where the business is owned by two or more people
(although equity partners will be treated as in salaried employment for the purposes of the financial requirement - see section 5 of this guidance). And a franchise allows a person the right to use an existing business idea.
I don't know what the difference is between a regular partnership and an equity partnership though. But if everything was set up properly, i.e., payslips, P60 forms, etc., I don't see that route being out of the question.
The Annex FM 1.7 also says that for self-employment outside of the UK, the reasonable equivalent for the requirements for self-employment in the UK should be evidenced. So perhaps you could put her on the payroll in the US if that's easier, and supply the equivalent evidence to them. Though there is not much guidance on what they would be looking for specifically. But I would assume to interpret it fairly literally, and supply information about your business registration in the States, payslips, tax ID information, taxes paid, healthcare contributions, etc.
I'm not sure if either of these suggestions make sense for you, but I figured I'd throw it out there.