I lived and worked in IA during 2019 (full year) while my wife lived and worked in Ohio. She moved to IA in August 2019 while still remotely worked from home for her employer in OH. So, she didn't have any income in IA and all her income was from OH. We'd like to file the Federal taxes jointly but then the online TurboTax wants me to pay tax to OH and wants her to pay tax to IA. Is that how it should be? I thought we only pay taxes to the states that we made money from. If that's not how it should be, is there any way around it?
It's not necessarily where you earned the income, but also where you lived. All your income belongs to your Resident State, and you get credit for tax paid to another state.
Since your wife lived part of the year in Ohio and part of the year in Iowa, technically she would file a Part-Year Resident Return to each of them, allocating her income by the % of time lived in each.
However, you could both file as MJF for Iowa and report that tax was paid to another state (Ohio) for the % of her income that was earned there.
She could then file MFS to Ohio and report only income and tax paid there (hers).
Click this link for more detailed info on filing multiple states.