Forgiveness doesn't always include forgetting or complete trust on our part - nor does it have to include asking that consequences not be imposed. It simply means, at the most basic level, a willingness to give up the natural tendency to condemn and to insist on personal retribution and to not carry around destructive emotions. Full, Godly forgiveness is described in terms of forgetting and agreeing not to impose deserved penalties, but God is the only one who really can see into someone's heart and make that determination correctly. We are to strive for the ability to understand and apply full, Godlike forgiveness whenever possible, but . . .
There are situations where we simply can't forget or completely trust without restriction - like someone who has sexually abused children. There's no way I would advocate anything that would result in leaving children alone with that person, even if I was 100% convinced the person had repented, and even if I really did forgive the person. You don't drop off an alcholic in a bar, even if that alcoholic was completely sincere in his or her commitment to abstain. I also would not advocate the person be freed from having to serve a standard (even if minimal) jail sentence for those acts, even with sincere repentance and my forgiveness. Some things actually do require imposed consequences, imo.
I believe we should strive to love those who have hurt us, but I also believe that is a very different thing than forgetting, not advocating proper punishment, etc. There are people in my ward and my stake and my job and in my extended family, for example, whom I really do love - but if their actions are destructive . . . Even if I can handle it, there's no way I'm exposing my wife and children to it, especially if it's just to prove that I really do love them.
I think we make many things much harder than they have to be. Idealism is great - but it really is only a theory, since none of us actually live in an ideal situation. It's OK to modify idealism to strike a balance with realism, as long as we never give up on the concept of the ideal and never stop looking for ways to get closer to it in whatever ways are possible.
Too often we conflate these things and end up thinking we can't forgive. Forgiveness is hard enough; throwing totally unrealistic and even destructive elements into the mix can make it impossible.