My daughter was supposed to receive a back payment check for survivor's benefits. When I called SSA they said I should have been got it, and they will but a trace on it. Is it possible that the department of public welfare could have took it. How will I Know if they did? I didn't sign any papers with them

A retroactive SSI check does go to taxpayer funded benefits such as welfare first.
You can try to get a copy of the paperwork from SSA, but if you know that you received more welfare than the retroactive check was, you can be sure that you won't be receiving a check. One branch of the gov't doesn't know what the other one is doing, apparently. The wheels turn very slowly sometimes.
(Your question is confusing, because first you say your SSI, then you say your daughter's survivor benefits. Those benefits are different from your SSI, so the answer to this question is best answered when you get the trace results. Also, my understanding was that ALL checks now are direct deposit, so for a minor child it would go into your bank. Is it possible that your info changed since your husband died?)