How can the wife be taken back if her family does not know that consummation occurred before the divorce, in order to avoid problems?

If you have been with your wife while she is still in her revocable waiting period (iddah rajiyah), there is no harm in you taking her back. If you fear informing her family of the truth, you can tell them that a private meeting with the wife has the same ruling as consummation, which entails the full dowry becoming obligatory, and the divorce that occurs thereafter is a revocable divorce. There is no lie in this, and you can achieve your objective with it.