Yes, you can file as Married, Filing Jointly on all returns (and it is easier). You would allocate the income in the state returns so that your income is not taxed by KY and your wife's income is not taxed by RI.
Answer the Personal info questions carefully, indicating both your and your wife's states of residence are different (if they are).
Your RI return would presumably list you as a resident and your wife as a non-resident (vice versa for KY).
If your wife decides to file MFS for KY, consider who the children live with when claiming them as dependents. You have a lot of flexibility, but it would seem more reasonable that the parent who has physical custody of the children would be most justified in claiming them.
