Well let me say for the record that I am not giving legal advice, nor am I permitted to.  But as for force, deadly force (in California) is only permitted  where the user of the deadly force has reasonable fear the force is necessary to prevent death or great bodily harm.  This notion that people have that you can go out guns blazing because someone's in your backyard is, in my experience, quite common, and equally incorrect.  The force you may use to protect property is described from various cases thusly:
1)  In law a person is only entitled to use that amount of force necessary for the protection of his or her property. 
2)  The owner of property is justified in using force or a deadly weapon to eject a trespasser only when it is manifest to one, as a reasonable person, that injury to the property is contemplated, and that the owner is then entitled to use only such force as is reasonably necessary to justify the attack or to protect the property. 
3)  The person who is acting in defense of his habitation must first use moderate means before resorting to extreme measures. But he may resist force with force, increasing it in the ratio of the intruder's resistance, without measuring it in golden scales; and whether he has used excessive force or not is a question for the jury. The question of the amount of force justified in repelling an assault or maintaining the possession of property is one peculiarly within the province of the jury. 
As for it being a "burglary" the question would be whether the coop qualifies as a structure.  I found the following cases:
1) Williams v. State 105 Ga. 814 (from Georgia):
A structure which is stationary, which is eight feet tall, covered with shingles, and inclosed with wire, erected for the purpose of the safekeeping of birds and fowls, is a house within the meaning of our code, which defines the offense of larceny from the house; and there was no error in refusing to direct a verdict of not guilty, on a trial for larceny from the house, because the evidence did not establish that the structure so erected was a house. 
and ...
People v. Coffee, 52 Cal.App. 118, from Stanislaus county, in northern California.
OVERVIEW: Pursuant to Cal. Penal Code § 459, defendant was charged with burglary for breaking and entering a chicken house with a felonious intent of committing the crime of larceny. Defendant was eventually convicted of burglary. Defendant filed an appeal that challenged his burglary conviction. He claimed that the information did not charge the offense of burglary because the house that he entered was for the use of chickens instead of human beings. The court agreed that at common law only the habitation of human beings could be the subject of a burglarious breaking and entry. However, the purpose of § 459 was to radically change the common law as to the crime of burglary. Section 459 made those who feloniously entered a building, other than a mansion or dwelling house, guilty of the crime of burglary. The court concluded that the information properly charged defendant with the crime of burglary. Finally, the evidence was sufficient that defendant committed the crime of burglary when he entered the chicken house with a felonious intent. The court affirmed the trial court's judgment.
Just one humble prosecutor's assessment of the law,
-Scott