What is the problem of the story hansel and gretel?

As far as it is possible to tell from the story, the witch is a witch and nobody's stepmother.

.....

Since this play is a dark and demented one, the mother does take over the place of the witch.

Even though they are two different characters and they do not inter-change.

The cruel intentions protrayed by the mother all evolves around child abuse and torment.

There are several different versions to the end of Hansel and Gretel. In one version the stepmother is still alive when Hansel and Gretel return and she regrets her actions and the family live "happily ever after" with the jewels that Hansel and Gretel stole from the witches house. In the Grimms version though, both the stepmother and the witch use similar phrases and the witch even says "they will not get away this time" implying I think that in the Grimms version they are the same person. So I think it depends on which version you are reading.