「せめて[親]{おや}でも[生]{い}きていてくれたら、こんなに[苦労]{くろう}しなくても[済]{す}んだだろう。」
First, this sentence is 100% natural, grammatical, etc.; It is perfect. As a Japanese-speaker, I know that without even thinking. (考えなくてもわかる) ← Hint #1: "Without" ≒「なくて」
I am thinking to myself: 「もし、user9771さんも[日本語話者]{にほんごわしゃ}だったら、この[文]{ぶん}を[理解]{りかい}するのに苦労しなくて済むのに・・・」← Hint #2
「Verb phrase + なくて/ないで + (も) + [済]{す}む」
= "can manage/survive/do/get through, etc. without (verb phrase)"
To express the "without" part, the verb phrase in Japanese MUST be in the negative form because you are essentially saying that you would make it if it were not for (something).
There is just no exception; The verb needs to be in the negative form.
"What will happen if I use the affirmative form by mistake?" asks my imaginary Japanese-learner.
That will change the meaning of the sentence completely!
Suppose you did not like eating raw fish but you were served sashimi as part of a course dinner.
You:「ボクのサシミ、[食]{た}べてくれない?そしたら、ボク食べなくて済むから。」
Guy:「[自分]{じぶん}で[食]{く}えよ。たった3-4[切]{き}れだろ?ささっと食えば済むんだから。」
You: "Could you eat my sashimi for me? So that I'll get through without eating it myself? (And it'll save me from looking impolite)"
Guy: "Eat it yourself, man! It's only a coupla tiny pieces, ain't it? Just swallow it down quickly and dinner will be over."
As you have seen above, I hope, if you used the affirmative verb form in front of 「済む」, the phrase would mean "(something) gets finished". "To end completely" is one meaning of 「済む」.
With that in mind, to me the whole thing, 苦労しなくても済んだ, now means "managing/making do and not having trouble"?
Exactly.
Considering the translation given by the book, how is it implied that the speaker is having difficulty?
It is actually "stated clearly", and not "merely implied". 「こんなに~~ない」 means "not this much". That would indicate there is an amount of (something) if not a whole lot, would it not?
Why is the negative form 苦労しない used here (but implying the speaker actually does 苦労) instead of the positive form?
I hope I have already answered this, but you just have no choice but to use the negative verb form to express "to get by without ~~ing". "Without" has a negative meaning, does it not? It just is not a verb in English.
In meaning, would you not agree that "Without (verb)ing" = "With not (verb)ing" even though the latter may not be used in real life?