Is it permissible for me to expel my wife from the home after she disposed of the gift I gave her by selling the gold and giving the money to her father, claiming he needed it, especially since we have children together?

Your words did not include a specific question. If you are asking about the ruling on your saying to your wife: "Go to your father's house, for I have no need of you," then this is one of the allusions to divorce. Divorce does not occur with it except with the intention. If you intended divorce by it, and it was not the third divorce and she was within her waiting period ('iddah), then you have the right to take her back without a new marriage contract.

If you are asking about the ruling on your wife's disposal of the gold you bought, then if you gifted it to her, it has become her property, and she may dispose of it as she wishes. If you did not gift it to her, or you gave it to her for adornment with her knowledge of your intention to take it back whenever you wished, then she has done wrong by selling it and is liable for it.