The fight for my room

Knowing that I'm back, Mi-Mi decided to come up to my room to pay me a visit. She sniffed around for a while not noticing Tiki hiding in the corner quietly growling. Then, the fight for my room began with Mi-Mi attacking Tiki. Then there was screaming and claws and growls and hisses. Not play fighting at all. Mi-Mi moves surprisingly fast for a 17 year old cat! I ended the fight by carrying Tiki away and Mi-Mi ran.

Things unfortunately, are basically picking up where they left off in January. Tiki is staking claim to my room because she sticks close to me and this is where she spent most of her time last time. Mi-Mi is attempting to regain her territory, which had been hers for 16 years. Sharing is not an option. Mi-Mi doesn't share. Mi-Mi doesn't like any other animals and Tiki doesn't like cats that are not friendly to her.

I'm not sure what to do. I can't really stop this unless I keep my door closed, but then Tiki would have no where to go or eat (Mi-Mi has been sleeping in the family room and eats downstairs). At least that would also solve the problem I've been having with Mi-Mi marking her territory, i.e. peeing, on my bed. I think I need Tiggy to act as a mediator, since he was friendly to Tiki last time and Mi-Mi is scared of him.