LIA will be the best bet for you as a good LIA will know the system in and out but i think it's unlikely there is a way for your mother to get residence at this time.
If they are ineligible you will have to wait to see what they do with the Parent Category in the future then work out a plan. OIA request's show that the minister has been considering what to do with the category so we may find out within the next few months if it will reopen. (Likely before July 1 as that is when INZ start's it's "new year" but no guarantees)