You obviously don't urgently need your refund. So I would file by mail and claim your daughter to get your full refund amount, instead of taking her off and e-filing, in order to get the smaller part of your refund sooner. You may want to use a mailing service that includes tracking and proof of delivery.
And, you will want to start assembling proof that you are entitled to claim your child as a dependent for 2020. In most cases, the dispute will be over which home did the child spend the most number of nights in 2020. To show the IRS that your child lived in your home more than half the nights of the year, the best evidence is letter from third parties showing your child lived in your home -- like letters from her doctor and dentist confirming appointments, or letters from school confirming bus routes or confirming that you have custody most days.
