@sjjestewart
Taxes between states are a bit complicated. Usually, you pay full state tax to the state where you actually performed the work (the non-resident state) and the resident state will give an offsetting credit. To give a simple example, if the only income was from the summer internship, and the CA tax on that income was $1500 and the IL tax was $1200 (because CA has higher rates), IL would give a credit up to $1200 (the IL tax). So I would only expect her to owe IL tax if the CA tax was lower. This is accomplished in Turbotax by preparing the out of state return first, so that any credit flows to the resident state return.
However, there may be some states that have an agreement to handle things the opposite way, so that she would owe full IL tax and CA would give a credit, reducing her CA tax. I just don't know the intricacies, as there are about 2000 different combinations of two-state income tax returns. I think @TomD8 may be helpful here.
We also need to reconsider her residency status. While her permanent residence is in Illinois, how long did she live in California? Just the summer, or is she a full time student there? It seems that California will consider her a resident if she physically lived in the state more than 9 months (273 days), even if she was a student living in a dorm or apartment. Filing as a resident of 2 states, rather than as a resident of one state and a non-resident of another, can raise additional tax issues.
https://www.ftb.ca.gov/forms/2023/2023-1031-publication.pdf
I'm also still unclear on the current demand. You originally said you owe $9 but you didn't specify where, I guess that is Illinois? So she paid more than $1000 originally, and now you are being assessed $9, and separately you are being assessed an underpayment penalty? If that is the case, it sounds like Illinois does not agree with the $8.66 shown in box 17. It's also unclear to me how she could have no IL income, but have $9 of IL withholding--I suspect the W-2 might be incorrect. In any case, my thinking is that IL is not giving her credit for the $9 for some reason, so they say she owes a further $9 payment.
As regards the penalty, if she owed more than $1000, then a penalty is well within Illinois' right to assess. I think her only option is to write the state and ask for an abatement on the grounds that this was her first time working out of state and didn't know the rules, and asking for forgiveness.
https://tax.illinois.gov/research/publications/pubs/penalties-and-interest-for-illinois-taxes.html#q...
However, before doing that, I would think about preparing a new set of federal and state tax returns for your daughter, making sure to prepare the California module first and the Illinois module second. As this seems to be for the 2023 tax season, you can use Turbotax Online which is "free to start" and you only have to pay if you want to file. (Or use the desktop program if you bought that already.) But make a new return (new login name, new file) instead of overwriting and changing the old return (for now). Make sure to do the California module first and that you indicate the correct California residency status. If the tax is the same, delete the return, you will just have proved the numbers are correct. However, if the numbers are different (because the credits flow differently) then you would need to go back to the original tax return file and prepare amended returns to show the new numbers. If the new numbers show she owes less to IL, she could claim a refund from the money she already paid, and if the amount owed is reduced below $1000, that should automatically cancel the penalty. File the amended CA return in the normal way but mail the amended IL return, along with a letter of explanation, to the office that sent the penalty notice, not the normal amending address.
And finally, for 2024, she will need to make estimated tax payments to Illinois or tell the internship to withhold for both states.
