Projecting a bit here
Be honest with your mum. DH and I have inherited an elderly Border Terrier who belonged to my DGran (DM mother) before she died. He was her constant companion and very much adored. My mother promised my gran that she would look after the dog because my gran was so worried about him.
Long story short, grans dog was dumped on DH and I with the immortal words, I don't want him, you already have 5 dogs, one more won't make any difference.
Whilst I would never see any harm come to Grans dog and he's happy and safe here, I really don't want him.
I resent the fact that my mother assumed that she could just off load him onto me because she could rely on the fact that I would feel guilty about offloading him elsewhere because he was my grans, and I REALLY resent and hate the fact my mother lied to my grandmother, which in turn makes me really resent the fact I have been dumped with the dog because the fact he's with me somehow in my mothers mind makes it OK that she lied.
Had everyone been clear and honest at the outset, maybe I wouldn't have minded so much about grans dog coming to live with us, as one more really does make no difference and I would have been prepared for it.
BUT it's the fact that my mother lied and then presented me with a fait acompli, knowing I wouldn't get rid of the dog. Made worse by the fact that he arrived when I was 38 weeks pregnant, and that my parents refused to look after him when I had an ELCS.
Yes, I am clearly projecting my own issues, but my point is that it needs to be settled at the outset, if not with your mum, at least with the wider family as to what is going to happen.