My soon-to-be Ex was awarded disability in WI almost four years ago. At that time, he was entitled to his amount of SSDI and each of his children were entitled to an amount as well. Each was paid monthly, just as he was. Our daughter's monthly payment was direct deposited into my checking account, since the state would not deposit into a savings, so each month I transfer her money over. The mother of his other child from a previous relationship was collecting child support. She was given the option of accepting ONLY the SSDI payment monthly, in lieu of the child support, or collecting both. She chose to collect both, using one to help care for the child (she was 16 at the time and was driving) and the other was placed in a savings account for her college costs in the future.
The original support was not reduced in any way, nor was her portion of the SSDI she received. In fact, our daughter's was less, since the first (oldest) child receives the maximum amount and subsequent children receive less...similar to how child support is calculated when multiple children from multiple relationships are the case.
The child support is based on 17% of wages, but when the provider is, for example, remarried and has another child and breaks from that relationship, then the "new" child receives 17% of what was left over once the first 17% was taken. I hope that makes sense lol. In my soon-to-be Ex's case, his oldest child's support was not reduced. He had to pay that after receiving his SSDI check each month.