Hi there,
I came across your post - really sorry to hear about all of the stress you are experiencing.
In order to apply for DCF with exceptional circumstances (which would speed up the process) - you would need to meet one of the criteria below. Do you know anyone in the US who could help to offer you a job? Or is there a medical emergency you could argue?
If your mom is just below the income requirement, it would probably best to get a second financial sponsor if you can.
Military emergencies – A U.S. service member, who is abroad but who does not fall under the military blanket authorization for U.S. service members stationed abroad on military bases, becomes aware of a new deployment or transfer with little notice. This exception generally applies in cases where the U.S. service member is provided with exceptionally less notice than normally expected.
Medical emergencies – A petitioner or beneficiary is facing an urgent medical emergency that requires immediate travel.
Threats to personal safety – A petitioner or beneficiary is facing an imminent threat to personal safety. For example, a petitioner and beneficiary may have been forced to flee their country of residence due to civil strife or natural disaster and are in precarious circumstances in a different country outside of the United States.
Close to aging out – A beneficiary is within a few months of aging out of eligibility.
Petitioner has recently naturalized – A petitioner and family member(s) have traveled for the immigrant visa interview, but the petitioner has naturalized and the family member(s) requires a new petition based on the petitioner’s citizenship.
Adoption of a child – A petitioner has adopted a child abroad and has an imminent need to depart the country. This type of case should only be considered if the petitioner has a full and final adoption decree on behalf of the child and the adoptive parent(s) has had legal custody of and jointly resided with the child for at least 2 years.
Short notice of position relocation – A U.S. citizen petitioner, living and working abroad, has received a job offer in or reassignment to the United States with little notice for the required start date.
Edit:
I also saw this note on the embassy website:
DOS may exercise its discretion to accept local Form I-130 filings for other emergency or exceptional circumstances of a non-routine nature, unless specifically noted below. However, such filings must be truly urgent and otherwise limited to situations when filing with USCIS online or domestically with an expedite request would likely not be sufficient to address the time-sensitive and exigent nature of the situation.
I think it's very unlikely USCIS would accept the DCF request in another situation outside the above list. BUT if you absolutely can't wait for the longer processing time, maybe you could include background that you are experiencing domestic abuse in your home in the UK and are concerned about your children. And you have a home/family/support network in the US. It's just an idea, but again I think it should be a very last option to consider.