When considering where both your parents should move to, can you perhaps find a place where they can be together? Some care homes do cater for couples, although, in the circumstances it might help if they had separate rooms.
Has your mum visited your dad in hospital? Maybe if she saw him in that setting she would understand that that is where he has gone and may not feel that she has been abandoned to this 'strange' place. If on the other hand she has significant memory problems then the kinder thing for her might be to not go into detail about the plans and what is going on. The 'blame the doctor' approach can often be the best one - Dad is in hospital and the Dr has arranged for you to stay here for a while, perhaps. Then when she asks to go home you can tell her that you will talk to the Dr and see what he says.
I don't envy your position right now and whilst your mum may not understand things, you are doing what is right for both your parents in the circumstances. Finding the right place for your dad is of course your priority and, although your mum might be vocal from time to time, you have the reassurance that she is safe and being well looked after and her needs are being met right now.
I hope you can get everything sorted without too much hassle.
Fiona