Sponsorship for family reunification

You should ask your nerest German embassy or consulate about the requirements.
That will give you a more definitive answer than strangers on an Internet forum, who might not be familiar with such individual details (and how your embassy applies them).

I don’t have a definite answer for you so like Beppi mentioned, best to contact the embassy/consulate in charge.

But I can give some background information. The German government promotes that families should be able to stay together. And that your wife is a EU national is of course a much better starting point than both being non-EU citizens.

The thing is that while EU citizens are allowed to live and work in Germany and usually have their spouse and minor children with them, they have to work and support themselves for at least around 2 years before being eligible for any form of public assistance. This is to keep every unemployed or unemployable EU citizen from simply coming to Germany and expecting to live off of the State.

But say your wife is in Germany long enough to now be getting public assistance, this might disqualify you from being able to come because it is pretty certain that they will eventually have to pay for you even if you presently have assets to cover a year or 2. In some matters other EU citizens will not have all of the rights of a German and even the non-EU spouse of a German can denied a visa if they don’t have not only the income but also a large enough accommodation.

But when they look at finances they usually look at income rather than financial assets – although I just assume that a very large amount of money will result in some kind of exemption. But one can blow through their money, or claim to have, and then suddenly be in a position where they have no assets or income. And like the requirements for a study visa with one having a blocked bank account, one can get a local sponsor to guarantee their expenses. But this is like signing a blank check and a huge risk for anyone to do it. And it usually has to be a sponsor in Germany – otherwise they have no way of holding the sponsor to their obligations if needed if they are in another country. So for a study visa anyway, this is usually rejected.

I am currently looking to work as an online English teacher through a platform that lets me set my own hours and pays through PayPal. This is not a job that will give me an employment contract as I would work from home and the company is based in another country. However it is a way for me to make money. Can I present this income in addition to my wife’s income to support my chances and the eliminate the possibility of me being considered unemployed?

Also to clarify my wife has been living in Germany for many years but has not worked but will soon. Therefore I don’t think she can get unemployment anyways. So I think I’m okay on that. Also, if my wife WAS employed for more than 2 years and still has a job that would make her ineligible for unemployment and then me being new to the country and not having lived here for 2 years yet also makes me ineligible. So why is that a concern for our situation?

Such an income (on a contract-less freelance basis) is only legal in Germany if you register a business, follow proper accountancy rules and tax all income (incl. MWSt or GST on the entire turnover and income tax on the profit).
This is a major effort and would require either near-fluency in German or engagements of professional business incorporation, tax and accountancy consultants.
The associated cost and complication make most such propositions financially unattractive, but everything else isn't legal.

Edited to add: As a self-employed person, you will also have to deal with (and pay for from your own pocket) health insurance and other social safety nets. Read about it in related threads!

The concern for your situation is that you, as non-EU citizen who has not been in the country long enough, didn't work and didn't contribute to the social system, will not be eligible for government assistance in case you fall into poverty. The authorities do not want anyone, under any circumstances to become destitute in Germany. Therefore you have to show that you (or your wife) have sufficient (and secure) income to rule this out. Otherwise you don't get the visa.

Note: The current threshold is around €10k/year per person. If your wife earns even less than that (which is far below German average), you will not be able to survive in any case.

What if I utilize 2 or more different platforms to teach wouldn’t I then technically be a “freelancer” and solve this issue?

Also I thought the minimum income was to ensure immigrants don’t become reliant on the state for benefits, not to ensure immigrants if they become destitute.

What I wrote above is exactly the situation of a freelancer.
If you freelance only (or predominantly) for one employer, you might be classified as employed even though your contract or agreement may say otherwise (in German this is called "scheinselbstständig") - and then the employer must retroactively pay all the social dues that they want to avoid by engaging freelancers. How this works with foreign employers is beyond my knowledge, but it would certainly not be easy, so a situation to avoid!

Nick639 wrote:

Also I thought the minimum income was to ensure immigrants don’t become reliant on the state for benefits, not to ensure immigrants if they become destitute.

What is the difference?
In Germany the authorities ensure, by the social safety net, that no-one becomes destitute (at least in theory - we could endlessly discuss about the deficiencies of this system).
If you are not eligible for that safety-net, you have to ensure it by yourself - or you won't get a visa.
Simple!

Nick639 wrote:

Also I thought the minimum income was to ensure immigrants don’t become reliant on the state for benefits, not to ensure immigrants if they become destitute.

This is circular reasoning. The reason they don't want people to be become destitute is because this is what leads to them needing public assistance. Seems rather obvious.

Nick639 wrote:

I am currently looking to work as an online English teacher through a platform that lets me set my own hours and pays through PayPal. This is not a job that will give me an employment contract as I would work from home and the company is based in another country. However it is a way for me to make money. Can I present this income in addition to my wife’s income to support my chances and the eliminate the possibility of me being considered unemployed?

Like Beppi mentioned, one will have to report all such income for tax purposed no matter where the company is based. And what you "might " earn is speculative, not giving any assurance, unless you have successfully done this already and can give hard figures and documentation to support your assumptions.

As an example one needing a study visa has to show enough money in a blocked account for living expenses. Despite that they are allowed some part-time work and might assume they will find a job, it doesn't change the requirements by lessening the amounts needed. The officials have to go on the worse case scenario that one will not be able to earn money. Anything earned actually will just defray the living costs which can easily end up being well over the amount required in the blocked account.

I also want to add that as an American citizen (according to your profile) you will need to inform yourself of the IRS requirements to file both tax returns despite being an expat and a FBAR form showing foreign held assets.

Also be aware that Americans are now very limited to banking services since banks world-wide have to report their information on a yearly basis to the IRS and many don't want to be troubled with this. Many banks will not take American customers, even if they hold an additional citizenship, even from German or a EU country. Some will allow Americans but only with a basic Giro account which is used for bank transfers which are the way things are done here rather than a checking account.

I have written extensively about this on other threads or one can look at the official IRS(dot)gov website.