I agree that it sounds more natural, and that the intended meaning is clear, using “even if.” But from context, I think the meaning is clear and the grammar is OK (if a bit unnatural) using just “if”. So, I wouldn’t call it wrong, just less good.

dbwlsld, you were on the right track when thinking that "even if" sounds correct. While you will hear English speakers use only "if" in this example, it is sloppy English. We can see this more clearly if we rearrange the sentence slightly: - Even if I wanted to do it, I couldn't. - If I wanted to do it, I couldn't. The first sentence means: even if I wanted to do it, which I don't, I couldn't do it. The second sentence means: if I wanted to do it, I couldn't, but I'm not going to tell you (or I don't know) if I want to do it or not. While the second sentence is a possible meaning the speaker wants to convey if (1) the speaker doesn't know whether or not she wants to go to the funeral or (2) if the speaker wants to be a bit circumspect with her mother, it is likely that the speaker KNOWS that she doesn't want to go to the funeral and is trying to be honest with her mother and tell her that she doesn't want to go to the funeral. Therefore using 'even if' is correct here.

John is right. This usage of "if" to mean "even if" is actually fairly common, but it's only used in sentences with the same structure as the one you quoted: "I couldn't X if I wanted to," "I wouldn't X if you begged me," "I couldn't X if my life depended on it," and so on. For example, "I wouldn't marry you if you were the last woman on earth" means "I would never marry you, under any circumstances, even if you were the only woman alive." The word "if" will NOT have this meaning if it comes at the beginning of a sentence. A sentence with the structure "If X, then Y" will not mean "even if." For contrast: [A] "If you begged me, I wouldn't leave." = I'm planning to leave, but if you were to beg me to stay, I would stay. [B] "I wouldn't leave if you begged me." = I am absolutely not leaving, under any circumstances, EVEN if you beg me to leave. (The meaning here could also be simply "if," the same as in sentence [A], but the context and the speaker's tone will usually tell you which meaning is intended.)

use " even if". It sounds more natural.