EEA residence card problem

[irenicus]

Background:

My wife and I want to move to the UK. She's from Uruguay and I'm Dutch and we currently live in Spain. We plan to move in 2 months, have booked an AirBnB for the first month until we can find our own apartment. She's a doctor and has a job offer from a hospital. In order to work in the UK as a doctor she needs registration with the GMC (General Medical Council). She's applying to be registered under "Exempt person status" since she's the wife of an EEA national (me). The GMC rejected the application saying I have not shown evidence that I'm exercising my Community rights. This is the form of the GMC we have to fill in: GMC form

Questions

What does it mean that I'm exercising my Community rights?
Do I need to live in the UK before being able to exercise my Community rights?

[secret.simon]

What does it mean that I'm exercising my Community rights?

Exercising treaty rights or Community rights means doing one of the following in an EEA member-state of which you are not a citizen;
a) working
b) seeking work (in the UK, this is limited to 91 days)
c) studying (also requires either CSI (private health insurance) or a non-UK EHIC card)
d) self-sufficiency (also requires either CSI (private health insurance) or a non-UK EHIC card)

As a Dutch citizen resident in Spain, for instance, you are already likely exercising treaty/Community rights in Spain.

Do I need to live in the UK before being able to exercise my Community rights?

Yes. You need to be resident in the EEA member-state in which you are exercising treaty rights. There are some exceptions, such as if you live in a border region and you work in one country while residing in another. But that will likely not apply in your case.

[irenicus]

My wife (Uruguayan) and I (Dutch) moved to the UK in late October. She has an EEA family permit that expired late March. We applied for a joint residence card since we are married. I just got a call that the application will be denied with the current documents provided as it doesn't show I'm paying taxes or social security in the UK. I work for a Dutch company remotely and they're still in the process of setting up the taxes correctly here in the UK. I have 3 days to decide whether to withdraw my application or not.

I would like to know what our best course of action is right now
- Do I tell my company to get things sorted and I reapply for the residence card?
- Or should my wife ask her company to sponsor her for a visa?
- Can she still stay and work in the UK while everything is in process?
- Can she freely leave and come back to the UK in the current situation as her EEA family permit is expired?