my mother is a widow and wants to remarry

The answer to your question depends on whether or not your mother leaves a will and how she manages some of her assets.
If your mother wants to maintain control over tbe assets that she brought into the marriage, then she needs to take steps to insure that those assets remain separate.  Texas is a community property state... and any assets will presumptively be community property.  If your mother co-mingles her separate property with the community assets of her marriage to new husband, then her new husband could make an argument that the funds have become so co-mingled (mixed up together) that it is imposible to tell which assets are separate versus community, and thereby, should all be deemed community property subject to division in a divorce or a probate.  If she takes steps to keep them separate-- then either she or her estate can prove that the assets are separate.  If your mom maintains the assets as separate property and she dies without a will, then her estate will be divided between her children and her spouse. 
If she wants to make sure that her wishes are honored, then she needs to leave a will.  In her will, she can gift any of her separate property.  This would include the proceeds of her life insurance policy and the rentals.  This would not include the rental income.  Any rental income is considered income of the community estate--so that will potentially go to her husband.  She can only gift one-half of her portion of the community estate. 
Dividing and preserving separate property can be a bit challenging.  Your mom may want to consider visiting with an estate planning or probate attorney.  They can assist her in making decisions and setting up methods for transferring ownership to her intended heirs via a will or another estate planning device.