Your wife and child cannot switch from a visitor visa to a Spouse visa within the UK and will instead have to return to the US and apply from there.
The minimum income requirement where there is a wife and a child is £22,400 taxable income.
For a self-employed person this is your net profit (income minus allowable deductions to give the amount you will declare for tax purposes). There is no grey area with regard to the amount - this is a minimum amount and your income will therefore not qualify.
You can, however, also use savings (or you can apply based solely on savings if you prefer. If solely using savings then the amount required would be £72,000.
If you have earned £22,000 declared taxable income then this will require you to also show £17,000 savings.
The equation to be used is to work out how much less than £22,400 your income will be, multiply that shortfall by 2.5 and then add £16,000. This will be the amount of savings required to meet the financial requirement by combining income and savings.
Please note that the minimum level of savings must be in your account at ALL times for a period of no less than 6 months.
Please let me know if this answers your questions.