It really has the meaning of to "cast", "let loose" an evil spirit. All creatures are subservient to God, and I see nothing wrong with God allowing an evil spirit between them as punishment.
Matthew Henry says this about the passage in his whole Bible commentary:
He sent an evil spirit between Abimelech and the Shechemites (Jdg_9:23), that is, they grew jealous one of another and ill-affected one to another. He slighted those that set him up, and perhaps countenanced other cities which now began to come into his interests more than he did theirs; and then they grew uneasy at his government, blamed his conduct, and quarrelled at his impositions. This was from God. He permitted the devil, that great mischief-maker, to sow discord between them, and he is an evil spirit, whom God not only keeps under his check, but sometimes serves his own purposes by. Their own lusts were evil spirits; they are devils in men's own hearts; from them come wars and fightings. These God gave them up to, and so might be said to send the evil spirits between them. When men's sin is made their punishment, though God is not the author of the sin, yet the punishment is from him. The quarrel God had with Abimelech and the Shechemites was for the murder of the sons of Gideon (Jdg_9:24): That the cruelty done to them might come and their blood be laid as a burden upon Abimelech that slew them, and the men of Shechem that helped him.
I'd really recommend getting a copy of e-Sword (http://www.e-sword.net
), and also installing Matthew Henry's Commentary on the Whole Bible also available from the site. I only got installed this commentary recently, and have personally found it one of the best.