If you are married to or in a relationship with a UK national and have a UK national child or parent for whom you care for full time, then it is almost certainly the case that you would be regarded as someone who was not exercising treaty rights.

The exact position of a carer, as an EU qualified person, is not straightforward. There could be a good argument to be made that you are a worker, or perhaps a self-employed person.

Although under UK immigration rules, 'carers allowance' is considered to be effectively a salary, this is not the case under the EEA Regulations.

If you are a single parent to a British child, then there may be an application that can be made under the UK immigration rules, but this is something that should be discussed with a lawyer. With the new settlement scheme now open, which is based purely on residence, there is no real reason to take this route.