When a parent is approved for SSDI there is an additional awarded for children based on the parent's benefits. This does not require the children be disabled, only that the parent is awarded SSDI. The award for children is 50% of whatever you get awarded.

For example, if you get $800/mo from SS then you children would be entitled to a total award of $400 per month (regardless of how many kids you have it's only $400 if you have one kid or 10 kids). As long as you remain on SS you will get the additional monies for your children until the youngest ages out. They also want to see that you claim the children on any annual taxes you file. If you are a non-custodial parent then they would direct the funds to the parent or guardian with custody.