MrsParker, really sorry to read your story. FWIW, I'm older than your mum, but I was bemused by girlnextdoor's post - unless she was trying to play devil's advocate. What your mum did was unquestionably wrong - whether it was your BF or your partner or your husband, and however unhappy she was with your father, it was still inexcusable and I am very surprised at Girlnextdoor's attitude.
I appreciate that your hurt stems from her betrayal of that unique mother-daughter relationship, particularly as she tried to lie about it. My only thought is, if she was really very unhappy, she may not have been thinking straight. She may even have been feeling on the verge of desperation and clutched at the pathetic straw offered - your no good BF. You said your father was so upset he almost killed himself - perhaps your mother was equally mentally unwell due to the bad place that she and your father were in. You may not have been aware of how bad that was, they may have been putting up a brave front for their children. That's me trying to find some sympathy or understanding for your mother, some extenuating circumstances.
However, that does not deny the hurt and betrayal you have every right to feel. You are very fortunate that your father is now happy and you have a partner who loves you. Please stick with Relate, perhaps discuss with the counsellor whether this is something you should find individual counselling for, as the problem is fundamentally not about your present partner, but about the past betrayals. My DP and I are having our 3rd Relate tonight. With us, also, the problems we are having are more to do with my DP's father, who is dead and can't answer for his actions. The first couple of sessions were very upsetting, but I'm told things do get better, you need to persevere.
One thing girlnxdoor said, you might consider, though, has there been ANY contact between you and your mother. Do you WANT any contact? Do you have any information about her present situation, ie is she happy with this man? If she was having some sort of a breakdown at the time, she may be bitterly regretting it now, but afraid of your rejection if she tried to build bridges.
So you may need to ask yourself, do you want to have it out with her and maybe reconcile, or do you want to deal with this without her involvement ever again in your life - which would leave you with questions about her love for you, which you will have to face up to never getting answers to. It's very hard to feel a mother doesn't love you - and maybe you need to make contact, perhaps through an intermediary family member, to find out exactly what was going on in her head at the time. It may be that she did and does love you, but that her mental state made her commit the worst mistake of her life, paying a heavy price by losing you. Alternatively, you may remember other things in your childhood and youth that lead you to think that your mother was failing in her love for you in other ways also - and this is something you would have to work through with a counsellor - such a mother would be better kept out of your life, so that she can do you no further harm. Only you can know this.
Follow your instincts, feel what you need to feel, do what you feel is right for you and your family now. Whatever you do, I do wish you and your partner the very, very best future together.