I would encourage you to read form I-601 instruction, page 12 in particular, which you can find on the USCIS website. You will need to hire a lawyer that specializes in I-601s. But the facts used to prove extreme hardship for the 601 need to come from your dad, the petitioner.
But essentially - Your mom must demonstrate that her qualifying relative (U.S. citizen/LPR petitioner) will suffer "extreme hardship" if she is not admitted. There is no getting around this, and is always required for an I-602 response.
Extreme hardship is a difficult standard to satisfy. Per USCIS: Common results of removal or separation — such as sadness, missing a spouse, difficulty adjusting — are expected and therefore not “extreme” by themselves. Therefore, the hardship waiver must be well-documented and carefully prepared. Again, emotional hardship is not extreme hardship.
For the unlawful presence, the inadmissibility expired February 2026. You'll need to confirm if that's accurate, otherwise you'll also need to include it in the 601.