Hi falvia,

And I don’t know how to be close without both of us being authentic. I don’t know what to do, or if there is something that I can do.

Yes. You can do it energetically without even going in front of your mom.

Practice the half-smile exercise.

What is the Half smile technique:

Half-smile is a technique borrowed from Buddhism, and it’s quick, easy, and free. … Begin to smile with your lips, but stop just when you notice a small amount of tension at the corners of your mouth. If someone were watching you, he/she probably wouldn’t notice any change in your face. It’s a subtle, tiny smile.

The half-smile starts with relaxed lips which turn slightly upward and a loose jaw and the eyes are soft and relaxed. Then half-smile spreads as your scalp and neck relax and your shoulders drop.

HALF-SMILE WHILE CONTEMPLATING THE PERSON YOU HAVE ISSUES WITH
Sit quietly. Breathe and smile a half-smile. Imagine the image of the person who has caused you the most suffering. Regard the features you hate or despise the most or find the most repulsive. Try to examine what makes this person happy and what causes suffering in his or her daily life. Imagine the person’s perceptions; try to see what patterns of thought and reason this person follows. Examine what motivates this person’s hopes and actions. Finally, consider the person’s consciousness. See whether the person’s views and insights are open and free or not, and whether or not the person has been influenced by any prejudices, narrow-mindedness, hatred, or anger. See whether or not the person is master of himself or herself. Continue until you feel compassion rise in your heart like a well filling with fresh water, and your anger and resentment disappear. Practice this exercise many times on the same person.

Source.

You will notice changes in the situation. Either both of you will have cordial relationship over the phone or maybe in person when you visit your mom. Or you may not have the feelings that you have troubled relations with your mother or maybe you may forget everything, or everything would sound/look like normal, or maybe this thing does not bother you anymore.