We are given four forms of the verb "estar" (to be) in the present tense. To help us answer the question, let's write the full conjugation of that verb in the present tense:
ESTAR
Yo estoy
Tú estás
Él / ella / usted está
Nosotros / nosotras estamos
Vosotros / vosotras estáis
Ellos / ellas / ustedes están
Now, let's translate the sentence and analyze its subject.
"Mi madre y yo ... muy unidas" translates to "my mother and I ... very close."
The subject of the sentence is "mi madre y yo," so we have to use the first-person plural (nosotras).
Therefore, the answer is:
Mi madre y yo estamos muy unidas.
Translation: My mother and I are very close.
What is interesting here is that we can determine the gender of the person who is speaking. Since "unidas" is written with an "a," the person who is talking is a girl / a woman.
We say that in Spanish grammar, "the masculine prevails over the feminine," meaning that in a group of women, if there's a man, then everything that refers to that group, for instance, adjectives, would be written in the masculine form. Here, if the person who is talking was a boy / a man, the sentence would have been "Mi madre y yo estamos muy unidos."