I have done a lot of rounds with delayed luggage, sometimes leading to me needing to go through the hassle of buying new attire, and a lot of it at times. Even for c. two day delays I’ve managed to get the airlines to pay up to the equivalent max SDR limit under the relevant Montreal Convention. If they refuse after being supplied receipts for local purchases and try to offer a lower amount, push back and push back repeatedly until you get what you deserve for the circumstances. Even offer to send the purchased goods to the airline and say you don’t want the replacement clothes but the money. If that doesn’t work and a complaint to the regulators doesn’t come with action fast enough or at all, you may have to take steps to avail to small claims court. In some parts of the US, at that point the airline may quickly collapse in its obstinate position and get to cutting a check or wiring the funds sought up to the limit of the Montreal Convention for trips covered by it.

It wasn’t that long ago that I had to buy two days of substitute formal wear for a rehearsal dinner and for the wedding thereafter. Got what I wanted and still have those clothes I would rather have not had to go run around and get in a crazy rush.

To bolster your case, present receipts and ask the relative to get online to send you a PDF of store transactions on their card that confirm the receipt charges. If they were willing enough to let the purchases go on their card, hopefully they are willing and able to get an online statement created and edited as they may deem necessary.

Good luck nowadays with taking all valuable clothes on board as cabin baggage, even if willing to do so as a passenger. Among other things, things such as 8-12kg limits on cabin baggage may mean that checking in luggage is going to have to happen anyway.