Should I get a letter of recommendation from my mother, who is a famous researcher in my field?

I would say no, this is a very very bad idea. Your mother going on about how likely you are to succeed will probably not carry much weight. What else would your mother say? If you were unlikely to be successful, would she say that? (even if she would, the perception of the people reading the letter will be that she would not)

Your mother is not a suitable person to write a letter of recommendation. Even people who know her professionally may not know whether she can write a really objective letter about you. One of your mother's collaborators might be a good letter writer, if they both know your work and are sufficiently independent of your mother to not have any conflict of interest.

Failing that, you can still discuss the projects you worked on with her, and perhaps indicate that you do not have a letter of reference for them because of the conflict of interest.

Although your professors have not worked with you as long, readers will put more trust in their objectivity. They have presumably worked with you as much as they have with other students at a similar stage for whom they are writing letters. They are better placed to know how you compare to your peers.

Not only would a letter from mother be discounted, it could have a negative effect.

It would simply beg the question "Why can this person not find someone independent to write a reference?"