Advising to give up while there's still room to negotiate sounds like bad advice. At the worst, OP could turn this into a learning excercise on how to negotiate in a tough situation, with zero downside compared to the advice given here.
This doesn't have to be a protracted legal battle, but reading up on documents they signed, figuring out their proiories (continue in biz? get at least some value out? etc) and negotiating in good faith is something that might come very handy later, in another startup, with much more to lose.
I think negotiation is good, if you're realistic about it, and if you actually value what you're likely to get from it. And I agree, they should quickly find an answer to whether they can be fired by their partner (they probably can, for reasons stated elsewhere on the thread, but it's very much worth getting a solid answer).
It's not me, but if it were, I'd approach the getting fired problem with "look, I build this. You can fire me, but you don't have money for adequate dev and average Joe will run it into the ground in two months. Your greed will make you lose everything", and also approach the investor (if they're hands on) with the same rationale.
Also agree with the point you made elsewhere - this can get gut wrenching (even without any lawyers getting involved) and if you're prone to dwell on negative thoughts, pretty damaging to your morale through the duration. Money spent fighting is not the only downside.
The downside here is what happens after trust is broken... You end up working for another 12 months at the company pro-bono, then get canned 1 month before your next cliff vesting.
I would take 10% for the first year of service and walk with it, not expecting anything. The angel put in 100K for 10%, and you worked for a year for 10%. very simple.
I would burn the entire thing to the ground and piss on its smoldering ashes before I would allow someone to take advantage of 11 months of my work just because he thinks he can make more money for himself if he positions himself as a solo founder.
"I would spend $15,000 of my own money and 8 more months of my life during which I deed control of my adrenal system to this stupid controversy and get little else done, and ultimately reach at best the same outcome as I'd have achieved walking away amicably, less expenses, before I would allow someone to take advantage of 11 months of my work".
Greater good/game theory argument. If we're all spineless, we just make it easier to be taken advantage of. Burning it to the ground is akin to MAD, but it only works if it's a likely outcome.
I'm not sure what I'd do but I'd view a 51/49% split as suspect from the start.
Their main claims to success based on OP's description are that they show up in search engine results and are only $60K in the red. If that's success in 2020 then I can launch a dozen successful startups by January 1.
They said they have 60k users. If you can acquire 12 * 60,000 = 720,000 users for 720k in less than a week I think you'll have a lot of people beating down your door.
the sad part is that they are right. I was in a similar situation and there really is nothing you can do. They don't own the majority share of the company to make the decision.