hello
@Pixel
a warm welcome from me too
it sounds as though your mum is sundowning, which seems to link with tiredness towards the end of the day
https://www.alzheimers.org.uk/about-dementia/symptoms-and-diagnosis/symptoms/sundowning
sadly, she seems to not be recognising your dad as her husband - it may be that she slips back in time and so expects to see the young man she married, rather than how your dad is 50 years on - so it's understandable that shd feels vulnerable with a 'strange' man in her home, and one who is treating her in a very familiar way eg calling her 'love' and sitting on the settee close to her, never mind sharing her bed ... wouldn't anyone feel anxious and unsafe
maybe your dad could tell her that her husband just asked him to sit with her while he ran some errands because you are all such good friends, then leave her be so she doesn't feel 'crowded'
sometimes the mind can be reset eg when your mum thinks your dad is a stranger, he says 'I'll go see if (his name) is around/home yet' and leaves the room ... he changes his shirt or jumper, makes a cuppa and calmly goes back into the room with her after a while with a smile and the cuppa and a treat - if it doesn't work, he backs off to keep her anxiety levels from rising and waits until she has settled
not easy for your dad, I appreciate - explaining, arguing, showing pictures of them together ... won't work - for your mum at that time she is right and trying to talk her round will only confirm to her that something is wrong, and it's not her - just think how you would react if someone who is not your partner were insisting they are! - so calm and distraction are the way to go
do also let her GP know, as karaoke Pete says, as some meds may help