I'm a man and I went through something like that 40 years ago, with my first great love of 8 years. I wonder if your wife is also your first great love? If so, and you are hers too, the power that her infatuation has over her is more understandable, and perhaps more potentially forgivable. But until she not only gets rid of all connection to the Zumba-guy AND feels and shows you Genuine Remorse for what she has put you through, you can't be expected to let your feelings begin to trickle away down the river of your life. To heal from this wound you will need her true and repeated expression of Remorse.
I know how terrible your feelings can be. But though I agree with Cathy that the decision is yours alone, I must admit that the RESULTS of your decision are NOT yours alone. For not only you, but also your wife and your 5 children will have their emotional lives altered by your choice: They will keep their sense of a secure and caring family household if you choose to act to contain the damage your wife's actions are causing through your feelings, or they will lose that sense of security with no power to prevent its loss, if you choose to leave the marriage. So how you handle your Entirely Heart-sensible feelings will have significant consequences.
Since you know who she's having this feverish emotional intimacy with, and you don't want her to continue, You Can Confront Him Again and Demand that He Cease All Contact with her (and you can damage his reputation if he doesn't). It doesn't matter what they both say, because his behavior is destroying your marriage, and neither your wife nor you want to give in to this destruction of your family that will also Damage the Faith that your 5 children have in the safety and sanctity of their parent-built family home-base. You can also insist that she go to a marriage therapist with you--preferably one with the training called Emotionally Focused Couples Therapy, because they treat marriages as being based on the Emotional Security of Secure Attachment, and her out-of-control actions now have undermined your security. (I studied the life-long marriage insecurity of children of divorce and their normally conflicted love relationships for my second doctoral dissertation completed in 1999.) Thus you have 2 allies besides your experts on JustAnswer.com (Zumbaboy & an experienced local marriage counselor/therapist) that can help you move her into terminating her infatuation and toward experiencing the Remorse that can begin the repairing of your wounded marital bond. You can also make an appointment for yourself with an Emotionally Focused Couples therapist (findable online--and I'll be one in Atlanta by January, as well as several women and another man or two) and insist that she go to a session BY HERSELF, so she can cope with her feelings without baring all of them to you at first. ONCE SHE GOES TO A THERAPY SESSION (she'll probably trust a woman more easily than a man) she'll probably have to start working on shutting down her flaming "unlived life" feelings for Zumbaguy, because she will understand what she's doing to her children if she can't regain control. I've seen marriages destroyed this way, and it doesn't have to end that way.
I felt what you're feeling when I was 28-29, but I had no legal marriage and no children, and my girlfriend was having sex with the boy (age 19). So I could leave after 1 year of struggling with the emptiness and within 5 years discover that I could love as fully again (even tho that love was doomed) and be glad I would never want to go back. I would not leave my real wife of 27 years now and our 24 year old disabled daughter if that happened again--but she and I have both loved another as well as we were able much earlier in our lives, so we're not foolish enough to let any attraction grow that much. You two probably haven't been through a long love that you lost before you got married, so "unlived life" and "passion with obstacles" are forces your wife has never faced before. Many of us therapists have faced them, and we can transmit those lessons and then help you both get over her emotional affair.
If Zumbaboy's actually gay, or just a mamasboy who can't love a grown woman yet, then he may also be gripped by "unlived life & passion with obstacles" as she is. You can ask him what his situation is, that is WHY he's so sure he won't get physical with her no matter what. You have every right to make him feel ashamed for the dishonor that he's doing to your marriage and potentially the harm to your 5 kids. You should use Face-to-Face encounters to maximize the shame he will feel because you are staring into his face when you speak. Of course you need to refrain from loud temper and violence, so that any illegal action (violence) that occurs will be grounds for Him facing legal action. And you also have the ability to damage his reputation, which could destroy his livelihood.
This confrontational stuff might sound pretty ugly compared to just getting a therapist involved. But you are fighting to save your wife from destroying the security of your marital bond, and that means you are saving 7 people including yourself. Most specially if a therapist is involved (and I could be more involved, but JA allows only email exchanges and downloads) your wife will eventually be grateful that you saved her from the worst mistake(s) of her life, and your children may never need to know how much your courage ("heart-stuff") to act (beyond your currently poisoned feeling-bond) for the security of your household has saved them from a lifetime of love-insecurity.
Obviously this is not a simple Q & A situation. So please ask more questions if you have any concerns. I have added to Cathy's answer because I have a lot more to offer on the subject, since I'm at least 20 years older. I'm grateful for the opportunity to apply my own hard-won experience to your threatened marriage-feelings.
Norman Brown, Ph.D., LMFT Florida