Is the husband Islamically entitled to reclaim the gold necklace that his mother gifted to his wife on their wedding day, claiming it is an inheritance and his share of it, and that its gifting was merely for appearances, knowing that the wife is keeping it for her daughter?

Since your husband's mother gifted you the necklace and put it on you, and did not mention that it was a loan, you have taken possession of it, and it is not permissible to retract such a gift after its acceptance, even if the mother were alive, for the Prophet, peace and blessings be upon him, said: "It is not lawful for anyone to give a gift and then take it back, except for a father regarding what he gives to his child." And if your husband's mother has passed away, your husband has no right to claim the necklace; for the death of the giver after the acceptance of the gift prevents its retraction. Therefore, you are not legally obligated to return to your husband the necklace his mother gifted you.