Please translate this saying

So the saying is as follows:

"Everyone is alone in birth. Everyone is alone in death. But no one can live alone in the time between."

みんなは出産で一人ぼっちである。みんなは死で一人ぼっちである。
しかし、誰もは間の時間で一人ぼっちする住んでません。

I have a feeling that the Japanese sentences above are wrong for one reason or another.

All help is appreciated. Thanks!

"Everyone is alone in birth. Everyone is alone in death. But no one can live alone in the time between."

One suggestion migt be:
誰もが生まれてくるときは一人。死ぬ時も一人。
しかし、そのあいだの時間を、一人で生きられる人はいない。

Several things you need to be careful about.
出産 is more "giving" birth," not when you are "born."
住む　is "live" alright, but more in the sense of "reside (in a location)," not in the sense of "living a life."
Also for a quote/statement like this, you need to pick the right "tone" for the whole thing.

I don't know if it was machine translated or put together word by word from a dictionary, but there is a limit without a real "human" translator :)

Roughly,
出産 means "to give birth", "to bear a child", so in this case, 生まれる is better.
みんなは have a nuance of "everyone (without me)", so みんな is better.
住む is "reside", so "to live between birth and death" 生きる is better.

For example, more natural Japanese
みんな生まれるときは一人ぼっちである。
みんな死ぬときは一人ぼっちである。
しかし、誰もその間を一人ぼっちで生きることはない。
Or
誰もが孤独に生まれる。
誰もが孤独に死ぬ。
だが、その間を一人で生きる者はない。

みんな is 誰もが(daremoga)
一人ぼっちで is 孤独(kodoku)に, 一人(hitori)で, 独り(hitori)
しかし is だが

As AK said, "一人で生きられる人はいない。" is exact.
I can't decide the last meaning.
It means the salvation or the restriction.

Is there a word I can use that means "birth" (the noun) and not "to be born" (the verb)? Similarly, is there a word I can use that means "death" (the noun) and not "to die" (the verb)? Or are the verbs given (生まれる and 死ぬ) the best words to use?

Kougeki,

The word 生 (read "sei") would be the noun for "birth," but it also means "life," so, no, I would not suggest replacing the verb with the noun. Also phrasing it "AT birth" or "AT death" with nouns would make the whole tone too stiff.

May I ask what you want the phrase for? At least for the first part, there is a more solemn sounding translation for it (using somewhat classical wording/grammar).

If you are thinking of wanting the whole thing concisely written in kanji or something, that is not possible in Japanese, I must say.