if she is joining you as non-EU spouse I believe she has the right to stay without registration 90 days per country. I am saying this because she does not have a schengen visa but a european residence permit issued as family member of eu citizen which - by definition - is entitled to travel together︀ or reaching the EU family member.
Based on my experience it may be really precious︁ having with you the Guide for EU border guards which covers basically all the technicalities.︂ Once you define the grounds for your spouse travel and you get in trouble on︃ the border it gets easier if you can immediately refer to their manual instead of︄ going through rejections, fines or deportation. This is always valid because for non-EU people the︅ border can be always a trouble due to different approaches followed.
Have a look below.︆ Take some coffee before the reading. It may get slightly boring.
https://home-affairs.ec.europa.eu/system/files_en?file=2019-10/c2019-7131-annex.pdfbtw, I would︇ not exclude that she could stay longer than 90 days in schengen (see below) as︈ long as she does not spend more than 90 days in a specific country (how︉ they could check it?)
I would avoid registration in any country if possible, particularly countries︊ having a definition of tax resident which is wide and based on simple registration (like︋ italy).
‘Members of the family of EU, EEA or CH citizens enjoying the right of︌ free
movement under Union law’ are, irrespective of their nationality:
the spouse (independently of︍ the sex of the spouse) and, if this is contracted on
the basis of the︎ legislation of an EU or Schengen State and recognised by the
legislation of the host️ EU or Schengen State as equivalent to marriage, the partner
with whom the EU/EEA/CH citizen has contracted a registered partnership;
UPDATE: CONFIRMED SHE CAN STAY LONGER THAN 90 DAYS IN SCHENGEN IF ACCOMPANIED/REACHING THE EU CITIZEN. Please check with a lawyer (point 2.1.2 of the document)
In the case of third-country nationals who are family members of EU, EEA and CH
citizens, they have the right of residence in a Member State for a period of up to
18
three months if they are in possession of a valid passport and are accompanying or
joining the EU, EEA or CH citizen, without any limitation︀ to 90 days in a 180-day
period.
To be noted that, third-country nationals who are︁ family members of EU, EEA and
CH citizens are entitled to accompany or join the︂ EU, EEA or CH citizen for
consecutive periods of up to three months per Schengen︃ States without any
conditions or formalities (except the need to have a visa for third-country︄ nationals
from a country subject to a visa requirement).
. When the family member travels︅ on his/her own, the normal regime concerning the
length of the short stay will (re)start︆ to apply, as the conditions for benefiting from
the facilitations concerning the free movement of︇ the EU, EEA and CH citizens and
their families are not met anymore.
The previous︈ stays performed in the area without internal border controls
accompanying or joining the EU, EEA︉ or CH citizen should not be taken into
account for the sake of the calculation︊ of the compliance with the 90/180-day rule
which is applicable to the short stay only︋
EXAMPLES (from the document shared):
An Indian national married to a French citizen may accompany︌ his French spouse to
Germany for three months, Spain for two months and Italy for︍ three months, thus staying
in the area without internal border controls for a total consecutive︎ period of eight months.
