Something is amiss here. If Social Security are saying they cannot act on actual benefit fraud, then this needs to be brought to the attention of your local MP and the papers. No excuses!
And whilst I think the largest number of them are fumbling, inept and unprofessional, you will need to ask your solicitor to request through the courts, prior to adjudication, a review from a CAFCASS officer.
It's always difficult to set aside the emotion, but in this instance, only deal with the facts. The courts will be able to make an informed decision which, hopefully, is in the children's best interest.
I wish you every success
Fr Bill