When is it love? When is it attachment?

I have this misunderstanding about love and attachment as they relate to one another. It's hard to put in words, so I'll try with some examples first. My understanding is that love is something you give away without expecting anything in return. While love where you need or want something from the other person (like for example, expect that other person to make you happy, or you want to control the other person in some way, or try to change them to be more of how you would want them to be, etc) is actually attachment. One example of true love I can think of is love for your children. You love them unconditionally. You understand they are their own person, with their own dreams, aspiration, thoughts, etc, so whatever they do, good or bad, you support them, help them, etc. You don't try to change them, or influence them, or impose your ideas on them, or have them accomplish the things you couldn't (e.g. I couldn't go to med school, but my child will), etc. No matter what happens, you love them because they are your children, and you love them no matter what they do. Taking that further, even in the presence of death, I still can understand love (at least I think I do). Everyone dies. Your children might die. And even if you love them and will miss them if they are gone, or suffer after they are gone, that suffering doesn't linger. You continue to love your children even after they are gone (or at least the idea of them or the memory of them). But here is another example. You love your partner. You think you love them like in the example above. But then they cheat on you with some other person. If you loved your partner unconditionally, you would be OK with that... I think. If being with someone else makes them happy, you should be happy for them, right? But in most relationships, you expect from your partner that they don't cheat on you, or to behave in a certain way. When that expectation is broken, you suffer. Arguments start, resentment, maybe violence towards that person. Is this because of attachment to the person and not love? Because we expect them, and demand, that they behave in a way that doesn't hurt us or make us suffer, that we are attached to the idea that your partner is only ours to have? So I guess, my question is this: What is love and what is attachment in a relation with your partner? What happens to love and attachment when they cheat with someone else? (for most of the people I know, death is less painful than being cheated upon; suffering caused by death eventually heals, but being cheated upon lingers for much longer). Can you truly love someone with no attachment so that no matter what they do, you do not end up suffering?