A lot of our parents generation were brought up to hoard in various ways - they lived or were born into the 1920s, 1930s or before when money was very tight and things were kept "in case they became useful" and some items were used again and again beyond sensible use.
With that background, and probably living that way as well,throughout their married life, it is not surprising that they hoard and it often only comes to light when either having to downsize or the pass away.
Items that are dirty, smelly, damaged etc should just be thrown straight out. Any gifts that are unused I am sure can be donated to charity shops or binned, because I very much doubt if your mother will know every single item in her possession. You can possibly get rid of other things, saying that they were damaged during the move.
The thing is, mum is having to make drastic changes not of her choosing and she is worried about your dad and about what living in a place where she knows no one, with the change in lifestyle at her age is most probably frightening for her, so that could be why she is lashing out at you and behaving like she is, by still grabbing hold of all that she knows.
Maybe, if you can, take her shopping for new items so she can feel that her new place is home and hers - even if it is just the odd rug or cushion , and in the meantime, edge all the tatt out the door!
It will probably take time, but I hope that she soon feels more settled than she does now.