Yet the police were never called, so there is zero police documentation of this incident. Trailer guys have no substantial evidence to demand compensation, especially two months later. There is no documentation that the OP even admitted guilt.
I’m not saying the OP should never go to the insurance company, I just don’t see how a claim can be successfully processed without proper documentation.
I see people keep carping on about the “OP’s responsibility“, while glossing over the trailer guy’s responsibility as well. When I got hit by a truck, I still had to provide a police report to my insurance. The other guy didn’t even have insurance. I couldn’t make a claim without that report. I also provided the receipt from the towing company. I wasn’t at fault, and yet I had responsibility to provide proof.
What do the trailer guys have to give to the OP that she can use to file?
I believe the OP had their heart in the right place from day one, but they are dealing with people who are trying to take advantage.
If it were me I would call the police because that's how I am but in my state that's not legally required given the situation the OP has given as it doesn't meet the requirements, I don't know what is the legal requirements for the OP's state.
A police report isn't required for a claim to be filed or investigated by your insurance company in terms of a blanket statement, it's helpful but not required. And police reports don't say who is at fault, that is determined by the insurance companies. It may be considered someone's responsibility according to their insurance company to call the police depending on the company and product they are under but coming from an insurance background there were plenty of claims I saw without ones and from an underwriting perspective for acceptability of new business sometimes police reports weren't available/done and that was one of the documents I would look at.
I don't necessarily disagree with your very last sentence but it's actually for that very reason I would not follow the advice of people here saying the OP needs to get more and more involved directly with these people asking for all this extra information. That may make them back off or it could make them do further harassment and could open up even more can of worms. So I would personally file a claim with my insurance company, provide them with the information I have and documents like the pictures and let them handle the rest.
As far as the time auto is a tad different but people may be surprised that on your home your insurance policy it's not uncommon to have 180 days or 365 days to file a claim. Storm damage is common to file after a time say you're getting your gutters cleaned and they notate damage, you could turn that claim in and your insurance company can look up the weather and determine if it's possible a storm 6 months ago could have caused it. For some of these reasons I'm less concerned about the time than others may be. It doesn't mean I necessarily believe the other party here just that the 2 month timeline is less red flag to me.
There doesn't have to be documentation of OP admitting guilt. A confirmation from the OP "did you admit guilt" should be met with yes, if the other party said "she told us it was her fault" it would then be corroborated by the OP. A police report isn't often going to say the words "Party A admitted guilt" it would be more like "Party A was reversing and made contact with Party B's trailer". Admitting guilt verbally is usually a no no because it can be used against you.
As far as your situation while this varies by state that is what your UM/UIM coverage is for if your state carries this coverage (subject to the restrictions of it) when you're involved in an accident with people who either do not have insurance or enough insurance. Some states allow you to sign paperwork rejecting such coverage (in return for a reduction in premium) and you'd be surprised how many times people still think the insurance company should cover them. I remember a coworker getting a call from a very distressed insured (we normally dealt with agents) because her claim was being denied. She signed rejecting of UM/UIM coverage and thus the insurance company wasn't covering her for that.
Depending on the jurisdictions the police may have their own rules. While probably not the case now in the early pandemic days it was more common for police to request non-emergent things to be walked in at a later time. I would still file a police report but it's possible in some places it's just not viewed as important enough if the issue was minor enough (as viewed by the police).
The reason people are talking about the OP's responsibility is because she can only control herself. You can't make the other party do xyz. It's quite possible if a claim is filed the insurance company would deny the other party's claim due to lack of xyz or it's possible they'll pay it and move on quickly. And while it may be a moot point the OP could have been the one to file a police report, the onus is actually both parties. It's not on just the other party here to have filed a police report. I think naturally people tend to not want to out themselves and thus may be less likely especially in a minor situation like this file a report on themselves as people might assume the injured (not physically but just ones with the more damaged property) should be the ones to get a police report for their vehicle.