You can't avoid having to exterminate insects and pests if they have invaded your home.
There's no avoiding exterminating bugs and vermin once they have made their way inside your home.
この場合、次のような言い方ができますよ。
ーYou can't avoid having to exterminate insects and pests if they have invaded your home.
「虫や害獣が家の中まで入ってきたら駆除せざるを得ない」
to exterminate insects and pests で「虫や害獣を駆除する」と言えます。
ーThere's no avoiding exterminating bugs and vermin once they have made their way inside your home.
「虫や害獣が家の中に入ってきたら、駆除せざるを得ない」
to exterminate bugs and vermin で「虫と害獣を駆除する」とも言えます。
ご参考まで！
カナダ 
