The first question is where is your wife's domicile? Domicile is a tax concept something like permanent residence, it is where the majority of her financial, family, social, legal, and other ties are. Where her doctor, dentist, voter registration, significant friends, church membership, and so on are located. No single factor is controlling, it depends on the balance of all factors. A taxpayer can only have one domicile at a time, no matter how many homes they have.
If her domicile is still with you in state A, and I think this is the most reasonable answer for your circumstances, then you file the following.
a) federal married filing jointly
b) a state B non-resident return. She must report income earned while living in state B only, and pay tax on it. This can be a joint return since you don't have income in state B.
c) a state A resident joint return. She reports all her world-wide income, including state B income, and you report all your income. You pay income tax to state A, but you get a credit in state A for taxes that she paid in state B, which limits double taxation.
If you want to argue that she has changed her domicile to state B, then you need to file state A as married filing separately and she files state B as as married filing separately, to avoid you both being taxed in both states. This gets complicated, especially if you want to file a joint federal return -- which you probably should do since married filing separately has higher tax rates and many deductions and credits are reduced or disallowed. We can give you more details on how to do that if you think that applies to you.
@Opus 17 wrote: "If you want to argue that she has changed her domicile to state B, then you need to file state A as married filing separately (MFS)"
That depends on the states. Some states require you to use the same filing status that you use on your federal return.
Most states still allow you to file Married Filing Jointly (MFJ), even if the two spouses have different residency.
Don't use MFS without comparing the net tax change of doing so.
What are the states? If they are reciprocal states, it could make a difference. Need to look at both states specific domicile rules. Although from what you describe, she is likely considered a resident of the new state. On the other hand, the family's primary residence is in the old state. Is her employer withholding for the new state?
All that said, based on what you have described so far, I would file a joint resident return for your state and a non resident return for her state. File the non resident return MFS or MFJ whichever works out better and is allowed.