As the gift giver I usually take responsibility for sending gifts back that don't work. (Although it hasn't happened often.)
I ordered my sister a Kindle case for Xmas that I found online and she loved, but it turned out to be too big for the Kindle Touch, which is what she got. I sent it back myself and gave her the $ to use for a case whenever she found another one she likes. (Cute ones are so hard to find!) She ended up finding one on Etsy shortly afterwards and ordered it herself with the money. I ordered it with my credit card so I don't really get how she could have returned it! If it was from a local store that would be another story.
Also, my sister and I both gave a friend some Riedel wineglasses from Williams Sonoma as a wedding gift, and when she opened them, they were broken! My sister took them back herself to get her some non-broken ones.
So in this case, given that it was from a mail order place and the MIL paid with a credit card, I think the OP's MIL should have handled the exchange and either given the OP $ for a wrap or found a wrap like the one the OP asked for.