No. You are not required to file a joint return (though you may want to). Since your military spouse is not a bona fide resident of Guam, and has a resident state (CA), you may choose to file separately. She would file a US and CA state return as Married Filing Separately (MFS). Her only CA taxable income will be the rental property income as CA treats an active service member with a CA home of record who is stationed outside of CA, as a nonresident; so only the CA source income will be taxed by CA.
You can file in Guam as married filing separately with only your income/deductions.
However, you can file jointly. Where you file depends who has the highest adjusted gross income. Here is the Publication 570 reference; check the general rules for military and the special rules for Guam. In this case you could file a joint return based on who has the higher adjusted gross income (AGI), you or your spouse. If you do, you file a joint return in Guam and include all income; there will not be US return filed.
If your spouse has the higher AGI, you'll file a joint US return and report all income and no Guam return will be filed.
CA allows a military couple to file a joint US federal return (or joint Guam return) and a separate state return with only your spouse's income/deductions. As noted above the only CA source income will be the CA rental income. (CA reference)
To help you calculate which filing has the best overall tax results for you, I recommend using a TurboTax desktop product. There in one product you can create the various filing scenarios and use the one that is best for you (Jointly or MFS).
You can also create and file a joint federal return and then create a "Mock" separate federal return for your spouse which would flow to a CA separate return. You would not file the "Mock" separate federal return as you are filing jointly at the federal level; you would only need to print/mail the separate CA state return. Here is a link with more details on the process.
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