J
Yes, you can accept the DWP offer and then request a new appeal, I would wait for the Mobility component to be put into payment before doing so.
Your request would again be made on an SSCS1, there's no need for you to mention the DWP's offer unless you believe that it would help you with being awarded the Daily Living component.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems