The answer to your question is that you can’t convince your mother-inlaw because your problem isn’t with her. Your boyfriend hasn’t been willing to redefine his relationship with her. From his point of view, he is getting the benefit of having both lover and mother. What he doesn’t understand is that his unwillingness to put some boundaries around your relationship interfere with how intimately you connect with him.
I suspect that part of the reason that your boyfriend’s mother feels entitled to continue to “mother” is that you live in her home and haven’t married. There may be good reasons for that but she is of a generation that generally doesn’t take a girlfriend as seriously as a wife, regardless of the number of years the couple has been together. It may also be that your boyfriend hasn’t shifted his primary loyalty to you instead of his mother because he hasn’t made the commitment of marriage. At 50, he may see no reason to change. The way he’s living his life works for him. These are just guesses and things for you to consider.
As long as your boyfriend is happy with the situation, you have only two choices if you want to continue in the relationship: resent it or learn to appreciate her care for the man you care about and develop a sense of humor about it. Living in resentment isn’t a very happy option so I hope you can embrace the latter.
I wish you well.