I would like to file as single, as my soon-to-be ex-wife does not withhold any of her social security income. Presently, my son lives with her, but my daughter lives with me. Are we able to both file with both children as dependents? Or can these children only be listed on one tax return as a dependent?
A child's SSN can only be used on one tax return. You cannot double dip and both claim both children as dependents. The IRS cares about physical custody. Who did the children live with for the most nights---at least 183 nights-- in 2024? The parent who had the child for the most nights is the custodial parent.
You can't file as single if you are still legally married. You can file married filing jointly if you agree, married filing separately if you don't agree to file jointly, or head of household if you provide a home for a qualifying person, usually a child dependent, and you were separated from your spouse before July 1, 2024.
For dependents, I will only talk about children who are under age 19, or who are under age 24 while being full time students. If your dependents are something different, you need to provide more details.
You can claim any child who lived in your home with you more than half the year (more than 183 nights). That sounds like your daughter. It may include your son, depending on when you separated. However, if your wife also qualifies to claim one or both children as dependents, then you can agree between you on who should claim the children. If you can't agree, you follow the IRS tie breaking rules.
The first tie breaker is which parent lived with the child the greater number of days. You have to add them up. Maybe you separated in June, so each parent has 150 days from January to June, then add up the days after that to see where the child lived the greater number of days.
If the child lived with both parents exactly the same number of days, the second tie breaker is who has the higher taxable income.
Note that if your wife qualifies to claim your daughter by reason of larger number of days, and she decides to claim her, that's final, even though your wife will likely get no tax benefits or refund if her only income is social security.