Accessing Universal Credit as a Carer EEA national

I am assisting a client who is a single dutch national with 2 dependent children ages 2 and a half and 18 months.  She came to UK in 2013.

Her youngest child has down syndrome, needs 24 hour oxygen and is fed via a feeding tube.  Client is in receipt of Carer’s Allowance and Child DLA for son (HR care).  Cl has been unable to access UC due to right to reside.  Not able to establish the permanent right to reside, derivative right to reside, extended family member nor retained worker status.

Are there any arguments anybody can suggest for accessing UC as a carer?

She has enquired with nurseries for childcare - but no nursery willing to take child on due to insurance purposes (child care needs).

Can someone with more experience than I on this fill in the gaps? This from GOV.UK though;

Primary carer
You’re eligible for a derivative residence card if you’re the primary carer of someone who would have to leave the UK if you left.

The person you care for must be one of the following:

a British child who’d have to leave the EEA if you left the UK
a British dependent adult who’d have to leave the EEA if you left the UK
a child from the EEA who’s financially independent with full health insurance (‘self-sufficient’)

From the sounds of your post, you have ruled out all of the conventional rights to reside.

You would be left arguing something along the lines of proportionality or effective citizenship and to succeed on that argument, you would probably have to show some basis for distinguishing the decision in LO v SSWP (IS) [2017] UKUT 440 (AAC) or else be prepared to go to the Court of Appeal on that.

Doesn’t look good tbh.