This is a child surpport order that was never paid, but now the father of my children was killed back in 2006 left oweing a lot of back child support

You are allowed to collect from the estate if there was a support order in effect. The problem is that you have waited so there may be no recourse from the estate. If he worked and qualified for SDI then your children can and should be receiving a ssi benefit because of his passing.

When he died, if he owed you money, you could have made a claim against the estate for the money.

So if the estate is still open ( very doubtful if it was 4 years ago).
If the estate has already been closed, settled and the money paid out, it is too late to claim against it.

You should follow Judy's suggestion on the SSI money