SSA does have access to earned income information - but not any earlier than three months after the wages are paid. And sometimes not until a year after the wages are paid. Same with unemployment. By the time they get the information, the SSI recipient is overpaid. More work for SSA. There are computer matching programs. Anything the IRS can find will be reported to SSA for SSI recipients. If the dollar amounts are off by a certain amount, then the office gets an alert and a long list of cases of SSI recipients with the mismatch. That's how SSA knows before you told them. But that also tells me that your wife didn't report your wages the month after you worked because then there would be no mismatch. If you worked in March and she reported it in April, then her May check would have been reduced. The reason the staff seems more interested in catching her in a lie is that it appears to me that she has failed to report your wages. So in doing so, she created an overpayment which is again more work. SSA has a responsibility And it is also possible that she didn't fully report that you were separated in a timely manner. I will tell you that it is easy to remove a spouse from a record, it is more work to add a spouse to a record.
It is probably true that SSA staff doesn't like to see claimants who fail to report, over and over and over. Sadly, it happens all the time.
If she tries to think of reporting events as the job duties she has in order to get an SSI check every month, she may find it easier to stomach. We all have to do job duties that we don't necessarily like.
The general rule is that income from one month determines payment two months later. There are exceptions. Wages you earn in June reduce her SSI in August. You may want August's income to only affect August, but that takes a crystal ball. How much are you going to make each month for the rest of the year? There are also cutoffs and limitations created by the US Treasury on when checks can be increased or reduced on the first of each month.
The earned income exclusion is the first $65 and 1/2 the remainder. There is also a $20 general exclusion. So if you had a paycheck with GROSS earnings of $500, the countable earned income is $207.50. But for unemployment, pensions, non-wage income, there is only a $20 exclusion so a $500 unemployment check, $480 would be countable. It is an incentive to go to work. Then there is an allocation made for you and your minor children and your court ordered child support. The rest is considered income to her.
I will say this again. In caps. THE TWO OF YOU WILL HAVE MORE MONEY OVERALL IF YOU GO TO WORK. Her SSI only has to be $1 for her to keep Medicaid.
Her SSI may have also been reduced when you were separated because of in-kind income. How did she pay all her food and shelter bills when the two of you were separated or did her family help her?
I can understand problems with grasping affecting many activities of daily life. But she doesn't need to lift heavy soup pots ever and maybe shouldn't have babies that she can't lift. And without transportation, it would be difficult to get bags of groceries home. But it doesn't sound to me like she can't be left alone for part of the day when you go to work or school.

