I’d like to quit my job at the children’s home because it’s too hard, but, at the same time, I don’t want to go burning any bridges.
Go ahead and carry out the task and establish the institution. To carry out and establish something is to institute it too. What do you institute? An institution.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.