After entering tuition information for my wife (filing jointly), it said we'd be getting a $4000 refund on tuition paid. But my return totals stayed the same. What's up?

There is no education credit or deduction that will get you a full $4000 in the refund.  For the education tax credit, the $4000 is the maximum qualified education expenses allowable for you to calculate the credit amount.  For the Tuition and fees deduction, it could get you up to a $4,000 deduction which only reduces your taxable income thus lower your tax bracket.  It is not a great tax saving.  The state taxes have nothing to do with this. 

If you want to know if your daughter meets the Rhode Island filing requirement, please read:

According to Rhode Island Instructions for Form RI-1040:

• If you are a Rhode Island resident and you are required to file a federal return, you must also file a Rhode Island return. Even if you are not required to file a federal return, you may still have to file a Rhode Island return if your income exceeds the amount of your personal exemption.

 

• If you are a part year Rhode Island resident and are required to file a federal return, you must file a Rhode Island return.

 

• If you are a Rhode Island nonresident who has to file a federal return and has income from Rhode Island sources, you must file a Rhode Island return.

“Resident” means an individual who is domiciled in the State of Rhode Island or an individual who maintains a permanent place of abode in Rhode Island and spends more than 183 days of the year in Rhode Island.

@KamiSawZe