Someone from the *old* board was audited - it happens now and then. Basically, they are just doing a random check. You likely can show that you paid more than you are getting to take care of your kids without too much difficulty.
There are a lot of living and entertainment expenses that qualify. Some are:
Rent (you said no mortgage, but your rent also qualifies)
Food (if you charge your groceries, pull out copies of the CC bills and circle the ones from supermarkets)
Utilities - light, heat, water, trash, etc.
For the above, you can use a portion of the expenses. If you have 2 kids, you can allocate 1/3 to each (the last third is for you).
Clothing - same thing if you charged them
Anything for school such as supplies, class trip costs, etc.
Entertainment - sports fees, vacations, etc.
Religious education fees
Medical copays, etc.
Some of your auto expenses (gas, insurance, maintenance) for getting them to the places they need to go - school, doctors, playdates, etc. Not sure how you would allocate this but submit it to SS and see what they say.
Basically, anything you spend money on your kids for should qualify. Just get the bills together, circle the amounts that relate to the kids and send it to SS. Usually, their share of rent, food, utilities will cover the lio's share of what they get, if not all of it.
Mike