Carly
At the moment, you will only be required to claim UC if you need to make a new claim for one of the benefits that now come under UC but if you are receiving the SD Premium then you are barred from claiming UC.
So, what you have suggested will work providing you do not need to make a new claim for HB when your mother moves in, I don't think that it will but we don't advise on HB on the forum so I can't state you won't for certain.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems