I think your daughter sounds lovely. And so do you.:)
I don't think she is being unreasonable about the Mii, or the bed.
If I was going to be away for a night, I'd at least expect someone to ask if it was OK with me if they wanted to sleep in my bed. I'd feel a little miffed if someone just assumed it was OK. I'd say yes, of course, but I would want to be asked.
I'd also not want anyone using my Mii, without at least asking first. Again, I'd say yes, because it doesn't mean much to me, but I can perfectly see how it could mean a lot to your daughter. Much older people than she would care quite a lot. (I hardly ever play the Wii, so I may be wrong, but isn't it possible to set up many different Miis, making it quite easy not to have to use someone else's?)
I completely understand why you want to be obeyed out of love, not out of fear of punishment. I never punish my children, and they do obey me. They also love me, but I don't actually think that that is why they obey. They obey me because they believe that obedience to parents is required by God, and that such requirement is because of God's love for them. I don't think that most humans obey other humans purely on the basis of whether or not we love them. Your husband loves you, does he obey you? Would you expect him to? How about other adults with whom you have a loving relationship, is obedience expected as an evidence of love?