I cannot be a therapist for her.
Why not? A professional secular therapist is trained to be client-centred. It is mostly about: (i) listening; (ii) acknowledging; (iii) when the time is right, asking the client about how they feel and what might possibly be their reasons for feeling that way; & (iv), when the time is right, asking the client what options or solutions they have considered to resolve their situation.
If fact, my sister just phoned me now about our mother, who we consider also has narcissistic tendencies, thus is very difficult to help. With our mother, she has so much pride, stubbornness & 'saving face'. I was saying how I wish our mother could communicate with me better. To be able to communicate more intimately with our mothers I think is a good thing. (My mother is 82 years old).
But you are 20 years old thus this could be more challenging for you. When I was 20 years old, I personally was 'clueless'. However, I am much older now and I have counselled or carried a few ladies through their dark times. I am confident in doing this because i have some experience.
I recognise that everyone is in care of their own suffering and that you cannot alleviate the suffering of someone else, only they can do that.
The Buddha never taught all individuals will be able to alleviate suffering. Most people rely on the companionship of others. These people, the Buddha called "puthujjana' or 'ordinary people' and 'householders'.
I would like to give compassion to her but I'm not sure how to go about that in a healthy way for both of us as our past had no boundaries, and I had felt that her emotions were my responsibility.
Her emotions are not your responsibility however you can offer to listen to her and to support her. While you are only 20 years old and may feel burdened by such a situation & responsibility, your mother probably sacrificed much for you; thus your time to support her may have come too early for you. But the Buddha taught, as children, we must support our parents, when they are in need, as they supported us, when we were children in need of love & care.
While sharing with me her feelings about this and having my shoulder to lean on, I recognised the suffering she is experiencing is tied with a struggle with her identity and past relationships (my father).
The above is to be expected. When a woman has a husband with whom she has children with, often this family unit is a strong source of identity. Keep in mind, mother carried each child for nine months in her womb & then birthed them. If a mother did not have such identity, she could neglect the welfare of her children/offspring. Thus, in Buddhism, it is right view to understand there exists 'mother & father' for the maintenance of human life. This is why divorce causes confusion & suffering for many.
My mother is in the midst of a break up with her ex-fiancé
As I inferred above, often, it can be difficult for a woman/wife/mother to feel comfortable marrying again. Often, they attempt to marry again due to loneliness & insecurity, which is not really the right reason to get married. Therefore, if your mother feels insecure in her aloneness, knowing you will be there for her to support her can make her feel more comfortable.
As said, we should not really have the expectation she can be like a Buddhist nun and get enlightened. Generally, certain individuals are born with a capacity for self-reliance and it is only these fewer individuals who can walk the Buddha's Path.
I am not sure how to lend a compassionate ear for her during this time
It is difficult & frustrating to listen to people's problems if you don't understand any solutions to such problems. In this situation, the listener can also feel lost & particularly burdened.
The Buddha taught about marriage and the mutual qualities two people should ideally share for a lasting marriage. If your mother feels insecure, desperate or humiliated (lacking in self-image; self-esteem) due to not being married, it can be helpful to understand what the Buddha taught about finding a suitable partner. Having such knowledge can overcome the feeling of being burdened when listening to the suffering & confusion of another. If the listener can remain unconfused, then the listener can also feel unburdened.
Such advice about marriage can be found in the following teachings:
Understanding/comprehending the above teachings can not only help a person find a suitable compatible marriage partner but can also help a person understand the reasons why their (past) unsuccessful marriage went wrong.