Can loving-kindness meditation help with self-compassion or a difficult relationship?

It can support both, gently. Because the practice begins with offering kindness to yourself, it is a direct way to build self-compassion, especially if you tend to be hard on yourself. Extending those same wishes to someone difficult will not erase real problems, but it can loosen resentment and help you hold the relationship with a little more ease. Go at your own pace, and it is fine to keep the focus on yourself for a while. StillMind can tailor the practice to where you want to begin.