The bolded is only half correct in general, and irrelevant in this particular case.
It's not irrelevant because the OP's father didn't have a will.
Many married couples own all of their assets jointly, therefore the assets pass to the other spouse automatically.
I disagree. Real property is typically titled jointly in a way that title will pass from spouse to spouse outside of probate. Same is true of bank and investment accounts and sometimes automobiles. Everything else? Nope. Texas probate law provides that a deceased spouse's interest in community property passes entirely to the surviving spouse, but surviving children get the lion's share of separate property. There are way too many unknowns here to believe with any certainty that, if the father didn't have a will, the mother would have gotten the entirety of his estate.
In fact, that happens more often than the assets being willed to the other spouse.
I assume you have no citation to any statistics that support this. In my experience, the following are common: (1) married spouses will their entire estates to each other; (2) married couples own most or all of their most significant assets in a way that has documented title and jointly with the right of survivorship. In a lot of cases, 1 and 2 are belts and suspenders. Also, it is not uncommon for the most expensive fights to arise over what an outsider might view as insignificant assets.
In this instance however, we are talking about life insurance with the wife as the beneficiary.
That's one thing that's being discussed, but it's not the only thing.
Therefore it would never have been part of the father's estate. It would pass to the wife outside of the estate.
I agree.
I actually have a younger sister. I know my father didn't have a will. My mother didn't either. . . . I am wondering if I open a probate case to get the proof I need that my brother did this, how much do would it cost?
No way for us to predict that, but you've got a potentially complicated situation on your hand. If the $150k in life insurance proceeds plus whatever other assets exist are important to you, then you need to sit down with an attorney to discuss the situation, and he/she will give you an estimate of what will be required to pursue it.