I worked for an extended warranty administrator for a little over 3 years, here in the U.S. Canadian warranty may be pretty much the same as one here. The warranties I worked with were valid in the U.S. and Canada. Anyway, OP and his daughter will need to read the mouse print on the warranty contract. If it specifically states, in black and white, no uncertain terms, the tires have to be rotated at that selling dealer along with all other maintenance services or they have the right to deny any warranty claim then OP very likely has no recourse.
The maintenance requirement is how a lot of warranty companies and dealers weasel out of paying claims, especially expensive claims like this. They use the contract to say "oh you didn't bring it in for every single little service so we can not verify the maintenance history, sorry we don't cover it." If that contract does not specifically give the dealer the right to deny the claim, then OP and his daughter need to first speak to the Service Manager or Parts and Service Director at the dealer. Not the service advisor, you need to speak to a decision maker at the dealer. If the dealer is unwilling to budge then OP can possibly call the warranty administrator directly but they will very likely stand behind the dealer's decision. In that case, a lawyer may be able to get the dealer or warranty admin to cover it but again, OP and the lawyer have to read the contract word for word and see if the dealer can legally deny the claim. I don't really know what Ford itself would say but it can't hurt to ask them, if it comes to that and if it is a known problem with that engine. A lot of times the manufacturer stands behind the dealer as well, even more so on a third party non-OEM extended warranty contract.
This all depends on how that warranty contract is written, it does not matter whether the lawyer or anyone else can force the dealer to prove that not rotating tires blew up an engine, even though anyone with the sense of a billy goat knows darn well otherwise. I tried to Google the Tricare warranty, did not get a lot of info, but what I did find was not good. A lot of warranty contracts are not worth the paper they are printed on and are nothing but pure profit for dealers because they use every trick in the book to weasel out of paying claims. If it's the dealer being so pig-headed about it chances are it is like a self-insured warranty where repairs come off the dealer's P&L. That is why they dig their heels in like this. Things like this are exactly why I quit my job at the warranty adminstrator. I got so tired of seeing customers get screwed over. I also got real tired of people screaming at me about it every day. I will never again work in the car business, not in any shape, form or fashion. I wish OP and his daughter the best of luck with this.