You only pay taxes in the state where you live when you got the distribution. Have withholding for that state or increase your withholding somewhere else like a job or make an estimated payment. 

You will only pay tax to your home state of MO.  That is not considered "PA source income". You do not need to file a PA return, because of the IRA distribution. 

By contrast, if you inherited her home and sold it, for a profit, that sale would be PA source income; because the ''asset'' is physically located in PA.