I am joining this thread a bit late. First, I am not sure I have read any of your posts, so welcome! You will find that this is a truly amazing, loving, caring, group that will sincerely care about you and your family, no matter what. I am glad to have you join us. We DO have other fathers, but they do not seem to post as much. It is wonderful to have another male point of view. Cause y'all truly do often see things differently than we do, and react to things differently that we do.
If you have a chance to sit down with your daughter and talk about this, tell her you love and miss her and she can come back if she wants to (if that indeed is an option), and/or that you would like to work on fixing what was damaged in the past. Right now she is at an age where she is seeing her parents and other adults close to your age or older as people. Of course she didn't think of you as a puppy or fish, but she only thought of you as a Father. This was esp true once the two of you were the only ones in your home after the divorce. Explain that you are sorry she was so uncomfortable and upset. Explan that no matter what persons are in your life, she is still your daughter and you love and cherish her. Ask WHY she left when she did and the way she did. Even if she screamed it at the top of her lungs as she left, ask her to explain. Ask why she didn't give you a chance to speak to her about it.
She needs to see you as an adult with the same adult choices and freedoms that she has, probably more. There is one thousand percent NO reason that you should cut SO out of your life or have her 'on the side' and hide her from your daughter.
By cutting SO out of your life, or your home, or keeping adult females you care about away from her so totally, you give her a ton of very bad things. She will feel a great sense of possession toward you. You will have actively taught her that after you divorce, you have no right to form any romantic relationship with anyone else. You will teach her that you are less of a person and are not allowed to have a person who is your peer to care about you. . Most of all, you will teach her that you cannot love another adult as a SO because there isn't enough love for both your daughter and your SO.
When would you stop doing what she wants in regard to your adult choices? Would you talk them over in detail so that she could make a truly informed decision? How sick would that be? When she has a breakup, who is to take control of her adult choices? If adults cannot have relationships after a relationship ends, then SHE is not supposed to date anyone or be intimate wth them either. Should you throw her out if she does have sex after a breakup? How long after each relaionship ends is an adult supposed to stay out of all relationships that include sex? Questions like these, at the appropriate time and place, might have a very profound effect on her, even if her first reaction is that you are nuts or is anger.
Rather than telling her to grow up (which I seriously want to do, but it would be counterproductive), ask her what she thinks you thought and felt when she walked like that? Was that a good way to handle things? How would she feel if, now that she is an adult, you walked in on her and immediately either threw her out of your home or you walked away from her for a period of months to years? Point out that she is, or will be at some point, her own person, your and her mother's child, a sister, an aunt, a niece,a cousin, a grandchild. Each of these roles requires her to not just care for one person and what they want/expect/like/dislike about the relationship, but to balance all of those roles and what is best for herself and for each person she loves.
If talking doesn't go well, or at all, I would go and talk to a therapist (therapist) to see what underlying issues could be factors. I would invite your SO when the therapist says it would be a good time, and also invite your daughter to join when therapist says it is time. If you can afford it, offer to pay for individual therapy for her, as well as for the two of you and the three of you. If you cannot afford it, check otu the free clinics or a university with a graduate psychology program. while you see a student for therapy, it is a grad student and is carefully supervised by a licensed therapist. Many places videotape sessions so that a professor can show your therapist things that might have been missed or misunderstood. They have sliding fee scales and are often very current with the latest resources and techniques in the field.
For healing to happen here, you are going to have to really LISTEN to what she is saying, and to really HEAR what she says and means. I hope this helps and isn't too wordy to get through.