How should I handle this situation
Easy, you have your answer:
person 2 told me to keep out of the situation and to trust him and person 1 [...] he told me to stay away because he was looking out for me.
Let them figure it out between themselves. Easy as pie
I told him it would be better for all involved to discuss a solution
No, it isn't. It's their requirements and they have to hash it out before they come to you. They don't know who the product owner is, and your getting paid for the extra feature will depend on who they decide is the product owner. If it's person 1, he requested it so it's good, if it's person 2, tough luck. Or that's what they'll say.
In that case you can push back by saying
- it's their problem for having unclear leadership in the first place
- demonstrating they were both acting as product owners (through emails etc.)
It's up to you to decide if the extra pay is worth the extra hours you will put in chasing it up. Imagine if you had another gig and had to choose between doing free work and doing paid work. What would you do?
This is the end of my answer to your specific situation.
The following might not apply to you but I'll leave it here for future viewers.
Getting additional compensation for redoing the product is not an option.
What they probably told you is that they don't wanna pay you for extra work. They might not have used those words, but that's the gist of it.
Let me clarify what I mean: There's a huge difference between "getting additional compensation is not an option" and "they don't wanna pay for it". The difference is that you don't do the extra work, and it's always the former, never the latter. If they want work from you, they gotta pay for it. End of discussion.
This would apply to you as well if you had a single point of contact, but you serve many masters; it is not clear who is authorized to ask for extra features, but I'd go with whomever's signature is on the original contract.
The most common way of dealing with it is offering a service package of X hours for Y amount of money, and forcing them to be included in the original specification of work. So the client agrees to pay upfront for features A,B,C and X number of hours for things that might come up.
If a feature is ambiguous, as has been correctly pointed out, you don't work on it.