You can check the Lea and Chaves County Deed Records for an Executor’s Deed from the estate of your wife’s father to her and her siblings. If there was no Executor’s Deed, you will probably want to obtain a certified copy of the entire probate file - or at minimum, his Last Will and Testament , the Order Approving the Will, the Inventory of the Estate, and the Final Order closing the estate. If no probate or administration was performed on your wife’s estate, you can file an Affidavit of Heirship with the Lea and Chaves County Clerks. Begin with your wife’s father, and break down the lineage of succession to your wife, to you/your daughter, etc. Include all facts - your wife is deceased, and yourself and your daughter are her surviving heirs, whether you were married when she passed, etc. The affidavit should be signed by a person who has no interest in the estate of your wife’s father, or your wife, but is familiar enough with your family history to swear to the facts. If possible, have two people sign a copy and file them both in each county. A quick google search will provide many Affidavit of Heirship templates, and as long as the facts are there, the format should not matter.
As to the question of royalty payments received by your wife’s siblings, I would ask the siblings what company they are receiving royalties from and contact that company’s Division Order Analyst to find out whether they have been holding your wife’s funds in suspense. If they have not, find out what information they need to clear ownership of yours/ your daughter’s mineral interests ( the documents mentioned above should be sufficient) and whether the undistributed funds are being held by the company or escheated to the State of New Mexico. You can hire an attorney to do all this for you, but if you’re willing to invest a little time and work, you can do most if not all of it yourself and learn quite a bit along the way.
Best of luck!