I apologize for the rather ambiguous nature of this question. I would like to know how to go about spending money to speed up my game's production.

First up, some context: I'm working on a game by myself using Unity. I've been dabbling with game development for a number of years but this game will be my first published title. My goal is to finish and release this title while my dad is still around, so I have a tight (but uncertain) deadline to meet.
I've got a chunk of money saved up, and I am interested in using it to fund my game development. It's not enough that I could hire a full-time employee, but it should be enough to contract out some specific jobs/tasks. But I can't quite figure out what I can really hire out for, and what the best use of my money would be.

I suppose art assets are an easy one to get outside help for. I already have plans to hire out for some select character assets (eg an original main character) but after that all my environment and monsters are coming from the Unity Asset Store. So all of my art assets are things I am already budgeting for. Likewise with sound and music.

But there's a lot more that goes into game development, and I'm trying to figure out what I could hire out for to speed up my game development. But I can't seem to find anything that sounds right to me.

For example, programming. I like the idea of hiring someone much better than me to handle my code, but I don't have the funds to hire someone through to release. And if I hire someone for just - say, a week - then when I have to make later changes to his code I'll be stuck because I won't know how to fix various problems without spending a crapload of time trying to learn someone else's code. I mean, maybe I wouldn't have a problem, but the risk doesn't sound suitable.

Maybe I could hire someone to build my levels, but this also makes me feel very uncomfortable. Good level design is something of an iterative process, and it doesn't feel right to pay a contractor to make a given level. If it needs to be revised or iterated again, I mean, am I going to pay him again? At some point it becomes unfair to ask for another iteration without offering additional payment.
Plus, it just really worries me to hand over my entire game's assets to some stranger on the internet. Especially since I probably can't afford someone highly experienced/trustworthy.

So that's all I can think of. Is there something else I've missed that I could hire out for? Is there something I'm getting wrong in my assumptions about these things I feel I can't hire out for?
I would really appreciate any guidance or direction here. How can I treat my project as a business when I don't have business money?

If you're going to pay someone money, providing the necessary assets to actually work with is not a big deal. Make sure there's a contract that does specify that you own it all, and it can't be reused for any other project without your prior written approval, to make sure it's clear to both parties what the expectation is.

After all, much bigger games with budgets in the nine digits of dollars hand over the assets to all their employees and testers every day!

When it comes to “paying for speeding up” but not having enough to actually pay real salaries: this means you can't pay to speed up as much.

Are you working right now? Do you have enough money to take time off or leave your job until you're done? That would be a #1 lever on how much time you can gain for working on the game, right there! That's “paying to finish it.” It also serves as a nice pressure maker so you're not tempted to grow scope, because, you know, you will run out of savings and the rent still needs to be paid, so better finish fast!

Finally, if you pay for a custom character, make sure you also know where character animations are coming from. A character mesh and texture and rig is all good and well, but without animations that go with it, and fit into the game, it's not going to be good.

Do what we did, and make an asset manifest.

Some spreadsheet document that outlines exactly what needs to be made, linking to the finished asset, maybe putting time estimates, and maybe associated costs. This will :

1. Help track production
2. keep everyone on the same page
3. act as a load bearing document for your project
4. calculate rough timelines
5. Calculate rough costs
6. help keep people accountable
7. Give a solid sense of scope
8. Act as agreed upon deliverable checklist

You don't say what your own skills are, but Art is usually the most time consuming and expensive thing in any game.

Sounds like your doing a 3D game?

Well, you'll also need to budget for sound if you don't want to get free sounds off online databases.

Sounds like you want to pay people to get this done as soon as possible, but it also sounds like you don't have too much money .

In my experience, to make a game, you need solid skills or leadership in art administration and code You'll need to fill out those roles or cover those skills some how.

When you say you want to do this so your dad could see, sounds like he has limited time left? If that is the case, you should sit down with him, and estimate how much time he has left. As said before, are you able to quit your job and work on this full time? most can't. Things generally take 2-4x times longer than expected, especially if you haven't done this before.

Are you willing to share the Revenue with people? If yes, than consider building out a team. And compensating key members. If you do this, get them to log and track their hours. Depending on trust, you might need to audit those time sheets.

It all depends on how much you want this, and how much money you have.

You don't want to run out of money half way and be stuck with a semi finished product that you can't do anything with.