There is a person in my life that I need to maintain a relationship with…and unfortunately, I find her comments and advice to border on the insensitive…
There is no way to avoid her. Other than playing a little song in my mind when she talks, anything else I could do? Oh, if I say anything to her, she most likely burst into tears because I’m critical.
I think you’re best off sticking to the Miss Manners methods:
When someone says something offensive, you look at them with incredulity and say, “Pardon me?” In other words, the look on your face shows clearly that this is an ettiquette issue, not an audiology issue, but that you’re graciously giving the violator room for retreat.
This should be a tip-off to a normal person to realize they have crossed a line. They either apologize–“Oh, I can’t believe I said that. That was out-of-bounds. Please forgive me”–or elect to say, “Nothing, nothing”, or else go ahead and say what they have to say in the full knowledge that it is offensive to hear.
If she gets the message, you let the matter drop and graciously go on with the conversation. If she doesn’t get the message, and the comment is repeated, you might reply in the following ways:
After my godmother passed away of breast cancer she said, “She should have had a mastectomy, why did she have a lumpectomy?”
You can say, “I wouldn’t know. Her health decisions were between her and her doctor.” Repeat as necessary until the subject is dropped.
Yet at the same time, “That was her destiny.” 
Silence is the best answer to comments like this. If she says, “What?!? I just said it was her destiny,” you can reply with “yes, I guess you did.” It is a comment that doesn’t deserve an answer. Don’t give it one. Let it just lie there, naked, without any support or recognition.
After the funeral, “Your uncle didn’t say hello to me at the funeral”
Although you want to say, “If he overheard you repeat the comments about his dear wife that you made to me, I’m surprised that all he did was ignore you”, you might say, “I wouldn’t know about that. I’m sure his grief is very deep right now.” Repeat as necessary until the subject is dropped.
After I had a miscarriage (my second) “Why did you try again so soon? Weren’t you supposed to wait?”
“Sally? Did you really just ask me that? That really isn’t any of your business.” Repeat as necessary until the subject is dropped.
When my son was born prematurely, “Well, she wanted the baby.” (meaning me)
“Sally? Did you really just say that? That really isn’t any of your business, and I can do without hearing that kind of comment.” Repeat as necessary until the subject is dropped.
When learning about my heart condition (minor) " You took a huge risk getting pregnant again. I know someone who died giving birth."
“Sally? Did you really just ask say that? That really isn’t any of your business.” Repeat as necessary until the subject is dropped.
There is no guarantee, of course, that she will ever wake up to the fact that her comments are inappropriate. With repeated exposure, however, she may figure out that she will not get anywhere with you by making these personal comments…no validation of her opinion, no defensiveness, no drama. She will just get a direct and unceremonious escort back to the land of appropriate, in terms that let her know she has dropped in value as an intimate.
Do not fall for the “burst into tears because
I’m critical” ploy. If she violates ettiquette, and you respond as ettiquette predicts you will, there is no reason for that kind of drama on her part. If she apologizes, accept the apology and graciously move on, but insist that the topic remain closed. If she decides to cry, you can simply say, “Sally, you don’t need to be upset. It’s just this: that is my business, not yours. We’re not going to talk about it. Let’s just drop it and move on.” She doesn’t have anywhere to cry from, unless you give her one.
You cannot win by getting sucked into an invitation to criticize her behavior in a general way. If she is not under your jurisdiction (employee, envoy, someone who takes it upon themselves to be your public representative, etc.) don’t ever presume to correct the manners of another adult. Stick to objection to each violation as it occurs, and insist that the topic remain on that violation…which is simply that you did not appreciate her comment, the topic is not open for discussion, and that’s that.
If she wants to call you “sensitive”, do not get into defending yourself or outlining what part of your personal life is open to her comments. Just repeat: “Pardon me? Sally, it’s my life, and I don’t want your opinion on it. If I want your opinion in the future, I’ll ask for it. Accept that, and let’s move on.” Repeat, repeat, repeat. Do not let her lure you into any other side issues or make it into a big interpersonal drama. Do not fall for manipulative ultimatuums. That game takes two to play. Don’t bite. Even if she says, “Well, I guess you don’t want to be friends, then” you can still say, “Sally, I don’t want your opinion on this topic. That’s all. Now, let’s talk about something else, and not blow this out of proportion.”
Do not accept any invitation to tell her about times when she was rude in the past. Rather, insist that “What is in the past, is in the past. If I didn’t say anything at the time, that was my choice at the time.” Resist any temptation to “parent” her on ettiquette issues, even if she asks. If she presses for advice, suggest to her there are books, but other than that, if there is a problem, you’ll let her know.
(If, by the way, she goes and reads all of the books and starts giving
you ettiquette advice, you always have the fall-back that no ettiquette expert in the world would dream of giving unsolicited advice. Remind her of that, and move on.)