No. As I see it it could be what would say a villain seeing his plan failing. He could say:

“Je l’aurais eu, sans toi à ruiner toujours tout !”

Splitting the sentence is weird in French, keep it as a single sentence.

“Je l’aurais eu, sans toi à toujours ruiner tout !”

Is correct too, but sounds less like the nasty guy whining, and a bit weirder too.

I would change the previous sentences slightly.

I’d much rather say “Je l’aurais eu, sans toi pour toujours tout ruiner !”

So “pour” instead of “à” and the order of the next words makes more sense.

As for “Without +pronoun verb +ing” it translates to “présent du subjonctif” e.g. “Sans que tu ne fasses” (“Without you doing”) -> Sans + que + pronom + verbe (au présent du subjonctif).

I would say: “je l’aurais eu sans toi qui ruines toujours tout !” It’s less literary though more elegant (it’s an alexandrine…).

I’m mostly surprised by the numerous bad translations proposed: “pour toujours tout ruiner“, “à toujours tout ruiner” : this sounds obscure in good French. The correct French verb, here, is not “ruiner”, but “gâcher”:
“Je l’aurais eu, sans toi qui gâches toujours tout”.

In french i would say

"Je l'aurais eu si tu n'avais pas tout gâché, comme d'habitude."

I am not english native, then I might have misunderstood your sentence.
I understood “Without you always ruining everything!” as, if the subject used to ruin everything he tries to manage

If “Without you always ruining everything!” means, that the subject ruined this business in particular, simply write :

"Je l'aurais eu si tu n'avais pas tout gâché."

“Ruiner” is an old use to translate “to ruin”, moreover if the speaker is angry or excited. You can also replace gâché (gâcher) with bousillé (bousiller) or pourri (pourrir) in a familiar use, or with anéanti (anéantir) or saboté (saboter) for a more formal use.