My mother-in-law insisted on taking my room card and key. Is this appropriate?

You can ask why you took this first. You have to listen to her reasons. If you think what your mother-in-law said is reasonable, you can give it, but if you think what her mother-in-law said is unreasonable. You can discuss it with your husband and let him speak for himself. After all, husband and mother-in-law are close. Husband says it's better this way. If you refuse to give it, it may lead to the breakdown of the relationship between mother-in-law and daughter-in-law, and may also lead to disharmony at home. So for the sake of family harmony, it's best for your husband to say it. If your husband is willing to give it, you can bear it. Harmony is most important. Don't quarrel over a little key issue. This is not good. So let your husband decide everything.