I feel really hurt by this! There are people all over Britain with my art in frames on their wall so I know I’m not terrible at what I do!!
Of course you are hurt!
Quite possibly, your DM has fallen into that trap of "oh it's just my kid's work, it can't be much of merit" which too many do.
BUT - this usually doesn't come from actually believing their DC are useless: it's a more complicated mixture of low self-worth coupled with poor object separation. Because they see their DC predominantly as an extension of themselves, & don't value themselves, therefore ...
Of course her comment stung. It was thoughtless, hurtful & thick.
Not saying your DM herself is any of those things! - but if she has some of the above going on, that might help you understand where the comment may be coming from.
However - this is about your feelings, not your mother's! & in your position, that comment would sting for a long time. It's obviously not an isolated incident, so you are likely feeling all the compounded misery of "death by a thousand cuts", which makes this latest one hard to distance yourself from.
Try this, initially as a thought experiment:
I feel really hurt by this! There are people all over Britain with my art in frames on their wall so I know I’m not terrible at what I do!!
Now imagine being with your mum, & saying:
"You know when you said I could get a "proper" DC portrait from cousin?
I felt really hurt by this! There are people all over Britain with my art in frames on their wall so I know I’m not terrible at what I do!!"
Then imagine where that opening remark might take a conversation.
"Mum, I get personal preference, & that's fine, but why is it your knee-jerk response that Cousin's portraits are "proper", but your own daughter's are not?"
Only you know your DM, so whether this is worth a try or not.
And as you felt it keenly, but didn't say it aloud in the moment, I'm guessing there are ...dynamics ... at play which constrained you.
But mull the above over, & decide whether you want to tell your mum what you told us. And whether it's enough to get it off your chest with a vent here, or whether you want to endure the discomfort of telling your mum how her denigration stings you, & asking her why she feels Cousin has the right to be viewed as a "proper" hobby artist while her own DD does not.