Again, there is too much self in this. "I allow myself to have peace of mind" and it could build conceit because I don't think we totally have peace of mind right now. This is where the compassion comes in, where we have compassion for ourselves in the present. By having compassion for ourselves in the present, it's also bound up with lovingkindness for ourselves at that present time because compassion also has this acknowledgement of the human potential. In addition, part of the wish is wishing Compassion/Lovingkindness for the person who we may become in the next moment, in the next moment and in the next moment. Part of that Compassion/Lovingkindness wish helps us bring up the effort to prevent by acknowledging our human potential at that time, to discriminate and find more peace, to let go of the anger, fear, worry and ignorance, etc. I find when I formulate it like this, I become clearer about what hindrance is preventing me from having it.
Having Compassion/Lovingkindness for yourself in the present moment, that's what having Compassion/Lovingkindness with the hindrances is all about. When we are doing the Compassion/Lovingkindness wish we aren't necessarily affected by the hindrances at that moment. So we are actually expressing lovingkindness at that moment by practicing the lovingkindness wish. I think that perhaps there may be a bit of resistance with this person to doing the Compassion/Lovingkindness wish. It would be helpful to look at that within yourself and see what is causing that, because hopefully again we would like to be able to have it for ourselves both in the present and in the future.