Но мне ещё на свете никогда
Побыть с тобой так сильно не хотелось
===
But I have never been like this. {This line is not needed, this is not what this line means}
I never wanted to be with you before as much as I do now. {This line covers both lines of the original, just break it in two}

————————————-

Я не твоя, решили где то там
Печаль объявит на меня охоту
И будет словно зверя по следам
Преследовать в любую непогоду
~~~~
I decided somewhere that I'm not yours.
I didn't want you to hurt me with sadness.
It would've been like a monster tracking me down
chasing me, no matter the weather.
—-> is not exactly what this means

It is all metaphorical:
Решили где-то там = They (like higher powers) decided
Печаль объявит на меня охоту = sadness will hunt me down (lit.)
И будет, словно зверя по следам, Преследовать в любую непогоду = It (sadness) will chase her, no matter the weather. Sadness is not the monster tracking her down, зверь here is she and the sadness идёт по её следам (like a hunter is following his prey following the tracks)

Hope it makes sense :)