いやがる is not 嫌がる but the -masu stem of 居る + やがる, which gives a nuance of contempt, curse or hate to the verb.
e.g.
とっとと行きやがれ(行く + やがる)
よくもやりやがったな(やる + やがる)
This is the key of your confusion, perhaps?
Incidentally, 居やがる and 嫌がる are easily distinguished in utterance by the pitch accent.
居やがる: accent type2 (the accent is on the second mora) /イヤ]ガル/
嫌がる: accent type3 (the accent is on the third mora) /イヤガ]ル/