The DL sentence is in the dative case, and for a feminine noun, you need "meiner".
Here is a table showing which possessive pronoun to use with which case/gender:
The first link describes the cases really well, and both links have great tables.
why is mother here the dative?
Because she is the recipient of the giving -- the indirect object of the verb. We mark the recipient of giving with the dative case in German.
do you separate both references to yourself ('ich' and 'meiner') into different cases?
Yes; mein has to agree in number and case with Mutter -- feminine dative, in this case: meiner.
so checking i have this right, 'ich' is 'nomative', mutter is dative and 'blumen' is accusative
Why is "I give my mother flowers" incorrect?
It is not. That's one of the accepted translations.
Do you have a screenshot showing that answer being rejected?
Did you report your answer as "my translation should be accepted"? Did you have a listening exercise or a translation exercise?
So lately, I've made mistakes and been marked correct, which is disturbing. Just now, it blithely told me that "Ich gebe meine Mutter Blumen" was correct. It's hard enough to get all these endings straight without being led astray like that.
If I'd noticed in time, I would have reported, but I didn't. Edit Oh, wait, I hadn't yet left that screen, so I did get to report that "my answer should not be accepted". Interesting that there is a button for that.
You are entirely mistaken. In English, when the indirect object comes with a preposition, the prepositional phrase comes after the direct object.
I give my mother flowers - correct
I give flowers to my mother - correct
I give to my mother flowers - incorrect