Look up the elements of the offense for both in the Penal Code and, if you are intellectually honest, you’ll see that neither of these would meet the definitions.
Criminal intent MUST be apparent and proven. It wasn’t.
To be convicted of criminal trespass in Texas, the prosecution must prove beyond a reasonable doubt that you entered or remained on the property belonging to another person without his or her consent. Also, you have to have been on notice that your entry was not allowed, or you received such notice but failed to vacate. A closed door would be notice that your entry was not allowed, to any intellectually honest person.
To be convicted of burglary in Texas, the prosecution must prove beyond a reasonable doubt that you entered a private residence or part of another type of building that the public did not have access to and while there you committed or attempted to commit a felony, theft, or an assault. She entered a private residence and shot a man, which any intellectually honest person would admit is a felony in anyone's book.
That is not correct. Mens Rea is not required. I will agree that normally it is, but not in this case and here is why: She entered the residence, without consent and committed a felony (30.02.a.3). It's not tied to the intent to commit burglary. It's tied to the offense against the person (19.02). And thus, 19.02 is then tied to 30.02 and that's why it's murder.
And no - I'm not an "arm-chair" lawyer. We have actually discussed this case at length in my criminal justice classes, taught by aw professors here in Texas. I am using my post 9-11 GI Bill to get my Criminal Justice degree after I retired from the military. We have GREAT discussions about the fact that they may have over-charged her. But as you know Texas does not have a 1st/2nd-degree murder charge. I was personally believing they would have been better off with a "Criminally Negligent Homicide" charge. But my prof and another law enforcement officer in the class explained very clearly why they went this route. It made sense and they predicted it would stick. They were right.