Do I have a choice to not claim her as a dependent if that becomes necessary for her school, since she could primarily still live in the US?
You have the question turned around. A parent is never required to claim a child as a dependent on their tax return. However, the child must answer "yes, I can be claimed as a dependent by another taxpayer" if they can be claimed, even if they don't want to be claimed, and even if the person who could claim them has decided not to claim them.
For 2022, your older child probably must check "I can be claimed as a dependent" on their 2022 tax return (although this depends on facts not in evidence). Assuming they could be claimed, whether or not you claim them is up to you. (I believe the FAFSA is looking for that answer on their tax return, even if you don't actually claim them.) However, the school should be able to assess their needs for your special circumstances.
For 2023 (to be filed in the Spring of 2024) it is likely that the child will not qualify to be claimed as a dependent (even if you wanted to), because they won't live in your home more than half the year. Under normal circumstances, a child away at college is considered to "live at home" because college is a temporary absence, but where the parent has relocated out of the country, it is probably not reasonable to consider the child to be living "at home" when the parent's home is a place in a foreign country where they have never lived except for short visits. (Unless the child moves in with you in a substantial and non-temporary way.)
