Is it permissible for the father, who is the guardian of his minor daughters, to use his deceased wife's pension, which is designated for his daughters, for personal purposes such as Hajj and Umrah, or marriage, or buying a gift for his new wife, knowing that his daughters live on his private money?

If the pension is the right of your minor daughters from their mother's inheritance, then you are not permitted to expand its use for purposes other than their benefit. Therefore, you should not perform Hajj or Umrah, or get married, or give gifts to your wife from their money. Let these be from your private funds if you are well-off; otherwise, you are not obligated to do so.