If it is true that you always worked and paid FICA taxes as an employee but failed to paye self-employment taxes for only two years, I find it hard to believe that you are not insured for SSDI since you (for persons over age 31) can have five years of zero earnings and still have enough credits in the ten year period before you became disabled. So, something is incorrect in your statement.

If you are only missing 4 credits, there is still the issue of what year you are referring to. 1990, 2000, 2007? SSA also has time limits on when you can correct your earnings record. Also, since you are apparently only paying these income taxes solely for the purpose of qualifying for SSDI, SSA may not believe that you actually performed work. There have been cases in which people file false tax returns for false self-employment solely for the purpose of having enough work credits.

Even if you had enough credits to qualify on your own record, if you are young and just barely insured for SSDI, it is possible that your monthly benefit would equal the family maximum and there might not be any money for your children. Also, not all SSDI benefits exceed SSI benefits. Depends on lifetime earnings.

Can't tell you the expected outcome of your plan, except there is a good chance it won't succeed.