"Guardianship" is probably irrelevant (see Opus 17's comment for an exception). For tax purposes, a stepchild is the same as a biological child, even after you are separated or divorced from the parent.
So, since the child lives with you, and you are her step parent, she qualifies as your "qualifying child" dependent* (not just a qualifying relative), assuming she meets the age requirement (under 19 or under 24 if a full time student).
Q. Is there anything I can do to claim her as she is my dependent?
A. Yes. If someone else claimed your child (she is "your child" for taxes) inappropriately, and if they file first, your return will be rejected if e-filed. You would then need to file a return on paper, claiming the child as appropriate. The IRS will process your return and send you your refund, in the normal time. Shortly (up to a year) thereafter, you'll receive a letter from the IRS, stating that your child was claimed on another return. It will tell you that if you made a mistake to file an amended return and if you didn't make a mistake to do nothing. The other party will get the same letter you did. If one of you doesn't file an amended return, unclaiming the child, the next letter, from the IRS, will require you to provide proof. Be sure to reply in a timely manner.
Winner gets the tax benefits; loser gets to pay the IRS back with penalties and interest. The custodial parent (that's you in this case) almost always wins. The IRS goes by physical custody, not legal custody. The non-custodial parent can only claim the child as a dependent if the custodial parent gives permission (on form 8332).
You can even file amended returns for 2019 and 2020 and claim her.
References:
https://www.thebalance.com/claiming-same-dependent-audit-risk-3193030 (audit discussion)
http://taxes.about.com/od/dependents/qt/Dependents-Audits.htm
www.eitc.irs.gov/EITCCentral/f886-h-dep.pdf (full dependent discussion including audit section)
*There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.
The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
A child (including step children) of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:
- He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
- He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
- He lived with the parent (including temporary absences such as away at school) for more than half the year
