Is what the mother gave to her two daughters during her lifetime, in terms of money and gold, considered compensation for what her other children took from her and did not repay—a gift and a donation, or a bequest—given that the siblings were aware of this and there were witnesses, and there is no written proof of the debt owed by the siblings?

If the money the mother gave to her two daughters during her lifetime was equal to what their brother and elder sister took, and their debt was waived, then there is no harm in that.

As for the gold that you bought with money and gave to your mother, there are three possibilities:

1. It was a loan to her, and its ownership remains yours, and it does not enter into the inheritance after her death.

2. It was a gift and a transfer of ownership to her, and she bequeathed that it be yours after her death. This is a bequest to an heir, which is not enforceable except with the consent of the rest of the heirs. They should consent in return for having been exempted from debt. If the bequest is denied, then you have the right to demand repayment of the debt, and they would be sinful for refusing.

3. It was a gift to her for the duration of her life (a lifetime gift/umra). Its ruling is that it confers ownership to the donee and passes to their heirs, and the condition (of returning it to the donor) is nullified according to the majority of jurists, contrary to Malik and Al-Shafi'i in his old madhhab.

Our advice to you is to seek mediation from someone who can reconcile between you and uphold kinship ties.