J.W.
Your mom cannot and should not depend on you for her social life. I understand how you feel, being an only child myself, my mom acted similar. But you deserve to have a life of your own, you deserve to be happy and I don't feel as adult children we owe our parents our whole lives and future.
Mom is going to have to act like the adult she is and accept this. Keep inviting her, that's all you can do. I know us telling you not to feel guilty will not make those feelings go away. But if she is playing these emotional blackmail games then you should realize what she is doing and maybe confront her with it. It shouldn't "hurt her" when you want to be with this man, that's just ridiculous. She is saying these things exactly to make you feel awful and guilty in the hope you will feel bad enough to drop him and run back to her. She is making you choose. Well, that's what she wants you to do. She wants you to choose her so she knows that you love her more than anything else in the world.
You know, the only thing you can really do is tell her you do love her with all of your heart, but you also love him and you deserve to be happy. Ask her if she wants you to be all alone when she is gone? Will that make her happy? Because that is what will end up happening if you make her the center of your world.