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Texas Penal Code §9.04

The threat of force is justified when the use of force is justified by this chapter. For purposes of this section, a threat to cause death or serious bodily injury by the production of a weapon or otherwise, as long as the actor’s purpose is limited to creating an apprehension that he will use deadly force if necessary, does not constitute the use of deadly force.

Texas Penal Code §9.41(a)

A person in lawful possession of land or tangible, movable property is justified in using force against another when and to the degree the actor reasonably believes the force is immediately necessary to prevent or terminate the other’s trespass on the land or unlawful interference with the property.

Taken together I believe this allows that a person may produce a gun to threaten, but not shoot, a trespasser. From that I can not see anything legally wrong with Mr. Carruth going inside to retrieve his gun while telling Mr. Read to leave.

Texas Penal Code §9.31

(a)A person is justified in using deadly force against another:

(1)if the actor would be justified in using force against the other under Section 9.31 (Self-defense); and
(2)when and to the degree the actor reasonably believes the deadly force is immediately necessary:

(A)to protect the actor against the other’s use or attempted use of unlawful deadly force; or
(B)to prevent the other’s imminent commission of aggravated kidnapping, murder, sexual assault, aggravated sexual assault, robbery, or aggravated robbery.

(b)The actor’s belief under Subsection (a)(2) that the deadly force was immediately necessary as described by that subdivision is presumed to be reasonable if the actor:

(1)knew or had reason to believe that the person against whom the deadly force was used:

(A)unlawfully and with force entered, or was attempting to enter unlawfully and with force, the actor’s occupied habitation, vehicle, or place of business or employment;
(B)unlawfully and with force removed, or was attempting to remove unlawfully and with force, the actor from the actor’s habitation, vehicle, or place of business or employment; or
(C)was committing or attempting to commit an offense described by Subsection (a)(2)(B);

(2)did not provoke the person against whom the force was used; and
(3)was not otherwise engaged in criminal activity, other than a Class C misdemeanor that is a violation of a law or ordinance regulating traffic at the time the force was used.

(c)A person who has a right to be present at the location where the deadly force is used, who has not provoked the person against whom the deadly force is used, and who is not engaged in criminal activity at the time the deadly force is used is not required to retreat before using deadly force as described by this section.
(d)For purposes of Subsection (a)(2), in determining whether an actor described by Subsection (c) reasonably believed that the use of deadly force was necessary, a finder of fact may not consider whether the actor failed to retreat.

So I believe §9.31(c) is where the crux of the case falls. From the facts (which are far from confirmed), it appears to be Mr. Carruth's residence. Others have said it was Christina Read's and although fewer had said Mr. Read. But presumably it's Mr. Carruth's.

If so, and if Mr. Carruth's statement that Mr. Read's sons were not present, then it would not appear that Mr. Carruth was breaking a law. Once facts are confirmed there's a possibility, though I believe slim, that Mr. Carruth could be engaged in kidnapping had he been harboruing the children of Mr. Read.

The provocation is less clear. Jennifer Read has claimed that this was somehow planned, that they intended to provoke, which could render the self-defense claim moot even if it was otherwise "reasonable". It would be interesting if she has evidence to back up the claim that could convince a jury beyond a reasonable doubt. I do not know how much Mr. Carruth, a still legally married man, can be held responsible for the provocation of his girlfriend at the time but I would assume very little unless deliberately planned.