I would end the relationship. If you had suspicions that means that this relationship hasn't been very healthy for a while. To many, sex is the most private and personal thing, and if shes going to share her most private thing with another man while in a relationship with you, and then lie about it, there must be a line drawn somewhere. A solid line that does not budge and is not persuaded or moved by doubt. Once this line is crossed the relationship is over. There will always be a longing to keep the relationship, a doubt in your mind about whether it is the right choice, this is why the line needs to be in place, and a clear line too. It is not a matter of pluses outweighing minuses, it is a matter of yes she crossed the line or no she didnt.
Having what seems to be an intimate relationship with another man without your consent or knowledge and then sending nudes to please him as if your not enough, and finally lying about it as if she can continue cheating and its ok. Is your line further than that? Or has she crossed it?