This is a very interesting question. A direct Adjustment of Status based on K-2 probably won't work as that will require an I-864 Affidavit of Support from him to cover them, which I'm assuming he won't agree to do. (Were they included as immigrants on the original I-864 for the mother? I am not sure whether it would be possible to use that now.)
VAWA allows a battered spouse or child (including stepchild) abused by a US citizen or permanent resident to self-petition. However, I believe that, in the case of a VAWA self-petitioning child, the child has to be themselves abused, and not just be the child of someone who was abused. If she was a VAWA self-petitioning spouse, the children could immigrate as her derivative beneficiaries without having been abused, but she didn't immigrate through VAWA, so I don't think that would work.
Another option is she could petition the children (with I-130s) as children of a permanent resident. It would be in the F2A category which currently doesn't have any wait for visa numbers. However, they cannot do Adjustment of Status because 1) since they are not in the Immediate Relative category, they need to be in status at the time of filing I-485, and their K2 status (which only lasts 90 days) has expired, and 2) someone who entered on K status is barred from Adjustment of Status through anyone except the US citizen petitioner who petitioned them. So this means they would probably have to do Consular Processing abroad. Consular Processing requires waiting for the I-130 to be approved, and then it goes to NVC and the consulate. This is a long process, and they could wait in the US until they need to go abroad for the interview, etc., but they need to be careful about unlawful presence. The children will start to accrue unlawful presence when they turn 18. If they leave the US after accruing 180 days of unlawful presence, they will trigger a ban, so they need to make sure they leave the US before age 18 + 180 days and then wait abroad for the rest of the Consular Processing.