How can the LPR status for dependent daughter be determined?

OP: LPR since June 2021

OP’s ex-spouse: LPR since June 2021 but left the US in December 2020 (card issued after six months after departure)

OP’s dependent (daughter, currently aged 5): LPR since June 2021 but left the US in December 2020 (card issued six months after departure)

OP’s and ex-spouse divorce (UK marriage, UK divorce) finalised in July 2022.

OP’s ex-spouse and OP’s daughter allegedly visited Florida in January 2024 on ESTA (as explained by OP’s ex-spouse) and did not use the GCs. However, when OP queries I-94 travel history for daughter, the list comes back empty (i.e. it behaves as if she is an LPR).

Can LPRs obtain ESTA? Does applying for one invalidate LPR status? Would CBP let you in and not query why you hold GC?

OP would like to determine the actual status for daughter, how can OP do so? OP’s ex-spouse is uncooperative at best and is in possession of both their GCs. OP’s ex-spouse states she wouldn’t renounce LPR status for daughter without OP’s explicit permission.

Does OP need to formally relinquish the LPR status for daughter to avoid any issues in the future?

NB: OP is applying for naturalization in 2026. OP heard of derivative citizenship for daughter but is doubtful since the OP’s daughter lived with OP’s ex-spouse in the UK (OP has court-sanctioned in-person contact time in the UK and pays regular child maintenance).

Many years back I was a member of the Immigration Law Advisory Commission of the California State Bar Board of Legal Specialization. We were responsible for drafting, administering and grading the examination for certification of legal specialists in immigration and nationality law.

This posting would make an excellent question for the legal specialization examination. (That said, some minor technical editorial changes would have to be made).

Unless they voluntarily filed I-407 to relinquish their green cards, whether they abandoned residence is not definitively "determined" unless and until they try to enter the US on their green cards. Although the green card is only a valid document for entry under 8 CFR 211.1(a)(2) after an absence of less than 1 year, and they don't have any other valid document for entry as an immigrant listed in 8 CFR 211.1(a), the officers have the ability to waive their failure to have a valid document for entry, under 8 CFR 211.1(b)(3), if the officer determines that they haven't abandoned residence. If the officer believes they are inadmissible, the are entitled to removal proceedings in immigration court, in front of an immigration judge, who will make a second determination about whether they have abandoned residence, and can let them in if the immigration judge believes they haven't abandoned residence. Under various case law, abandonment of residence is a subjective determination that looks at a variety of factors, not just length of absence alone. My opinion is that they have likely abandoned residence in this case, but it is still theoretically possible that the immigration officer or immigration judge will determine that they didn't, and let them in.

This indeterminacy and theoretical possibility that they can still be admitted as permanent residents is also the reason why the IRS will continue to consider them resident aliens for US tax purposes (and thus subject to US taxes on their worldwide income), for the rest of their lives, unless and until they file I-407 or there is a final judicial or administrative determination that they abandoned residence. Them merely being outside the US for a long time or letting their green cards expire is not enough to end their tax residency. The IRS Publication 519 section on the Green Card Test has a note:
Just because they entered on the Visa Waiver Program or visitor visa does not necessarily conflict with their permanent resident status. 9 FAM 402.2-4(B)(10) describes a rare case where a permanent resident who has been outside the US for more than 1 year but has not abandoned residence, might get a B2 visitor visa for an emergency brief visit to the US, if there is insufficient time to get an SB-1 visa.

Derivative citizenship for the daughter won't be possible if she is not "residing" in the US or is not in the custody of the US citizen parent (not to mention the issue of her probably not being able to be admitted as a permanent resident).

The mother and daughter left the US in December 2020.
I thought that after a year or so of NOT living in the US your Green Card expires
(Just like you Indefinite leave to Remain status expires in the UK if you leave for longer than 2 years)

The card expires on the date written on the card. But the card and the status are separate. It's possible to remain a permanent resident even if the card is expired, and it is also possible to have abandoned residence even if the card is unexpired. Abandonment of residence in the US is a subjective determination. There is some case law to guide it, but there are no black or white rules. It is possible to be admitted back as a permanent resident after an absence of more than 1 year without a Re-entry Permit or SB-1 visa, and it is also possible to be found inadmissible for having abandoned residence after an absence of less than 1 year.

Thank you, all. As for the OP’s own N400 application, does this cause any convolution?

Why do you think the status of your extended family have a bearing on your citizenship/naturalization application? If you naturalize before the 18th birthday of your children who are already holders of a valid green card, then they will be US citizens as well.

BTW I'm assuming you are addressing yourself as the OP.

Only if the child was 1) residing in the US on the green card and 2) in the legal and physical custody of the OP.