Unfortunately you would be held at fault. Whether it's a canoe off the roof of your car, a piece of your car; like a wheel, a trailer that breaks away, or a piece of debris out of your trailer.... it's your fault.
a few questions:
How bad is the damage to your car?
How bad is the damage to the van?
What driving record (star rating) are you currently receiving on your policy?
Depending on your situation, if you have accident forgiveness etc, you may want to just put the claim through.
Both the damage to your car and their van would be covered, the damage to your car paid by your insurance co., the damage to the van paid by their insurance co.(that is the premise of the "no fault" insurance system). All you pay is your collision deductible. (that is if you carry collision coverage) If you have accident forgiveness your premium may not be impacted much if at all.
If you put the claim through your policy AND you are able to prove the shop was negligent (which is exceedingly difficult) your insurance company may sue the shop to recoup the claim costs and waive the fault against you.
If the total damage price tag isn't too much and you don't have accident forgiveness then you may want to pay out of your own pocket to save the increase on your future policy.
I would tell the van people that you would consider paying for the damage yourself. Ask them to get 2 quotes for the repair. (even if you go through insurance these are good to have).
If you decide to pay out of pocket, it's a gamble. The van owner and all of it's occupants have 12 months to decide if they want to claim injuries, EVEN IF YOU PAY FOR THE DAMAGE.
I've seen people get scammed where the person they hit seems very happy to take a reasonable payment for the damages, takes the money then reports the claim to their insurance company anyways and often says they are injured. They get double paid for the damages.
There isn't much to do to protect yourself. Some say pay by cheque so you can prove you paid and that they cashed it and on the back of the cheque write "I accept this cheque as full compensation for damages and/or injury for the incident on yy/mm/dd" so when you get the canceled cheque back bearing their signature you have a kind of disclaimer. Others would suggest you go to the shop and pay on the owners behalf.
I once paid for an accident and it showed up on my record anyways. The person I hit called their insurance company to see if it was legal for me to pay for the claim, they said "sure, what was his plate #" and put it on my record.
The advice I give my clients is this: The only damage you should pay for out of your own pocket is your own damage. Like if you hit a curb, or tear your side-view mirror off pulling out of the garage. Use your policy to protect you for being scammed by others. That is what accident forgiveness is for. Some insurance companies will even ignore 1 claim that the other party reports but you pay for your own damage.
FYI If any involved party puts a claim through their insurance, your insurance company gets notified.
Last question: Did you report your engine swap to your insurance company? (you don't have to answer that one, I'd rather not know
If not, first, consider yourself extremely lucky that the wheel came off at a low speed and didn't injure anyone. In circumstances like that, the police immediately impound your car (no time to undo the swap) and the insurance company goes over your car with a fine tooth comb and would have voided your policy for "material change in risk" or "misrepresentation" and denied your claim and any associated legal defense costs. Going forward, re-consider what you have disclosed to your insurance co. because they aren't going to pay for anything significant, especially a lawsuit.
My advice to you is: call your agent or broker and discuss your options. Ask, hypothetically even, what the impact would be to your premium. Will they ignore the claim if you pay for your own damages. And make a well educated decision from there.