Dragonfly, I'd be surprised if the legal systems in the two countries couldn't decide where domicile is since that's the key to deciding where the divorce takes place. There's nothing stopping you from filing in ten or twenty places but you need to get sorted as to where it is going to be rather than commencing proceedings in one place while she (or he) commences in another.
Bad as it gets, this needs to be sorted out. As does an interim plan for finances while in separation.