Q: Is there an advantage in filing for divorce first?
There is no specific advantage for filing first, but filing in general will give you an advantage. By filing for divorce it puts a restraining order on the community funds to make sure there is no fraud or misappropriation of the community funds. The community money can be spent for essentials only. This may be worthwhile for you since you are alleging there is theft of money going on. If that money is community property, you can protect is by filing and having her served.
If you are seeking the house as part of the settlement, you may want to consider living in it. If you are seeking the house as a condition of the settlement, then you should be living in it not her. If not then you need to ensure that the household bills are being paid especially if your name is on them.