A: It’s a good reminder that (well-meaning, unconscious) interrupters are unlikely to be extremely sensitive about having their behavior pointed out, but I don’t think the letter writer wants to have the kind of relationship where the two of them both spend equal time interrupting one another.
The letter writer wants their mother-in-law to stop interrupting, and I think that’s a reasonable request. A: "Hang on, I wasn’t finished talking." It sounds like your mother-in-law doesn’t realize how rude she’s being, so you should let her know!
Your mother-in-law probably won’t even notice if you interrupt her back, like Prudie suggested, and will be very comfortable with you insisting on finishing your thought. And acknowledge it in the moment; since you consider yourself close, feel
free live adult chat to also pull her aside and say, "You may not have noticed this, but you often interrupt me and others when we’re speaking, and it sometimes makes conversation dif***ult. Ask yourself what these grudges might be protecting you from, what you’re afraid of, and how you would want to feel and behave in a future romantic relationship.