Letters of Administration with Will Annexed

We have inherited a Will where both executors have died. The Residuary estate has a life interest to T’s wife for life or two years whichever is sooner. At the expiry of this date the estate reverts to T’s daughter.
Who would be the administrator. Our thought is the wife as she has the current interest would have the best claim, but as there is a life interest, she would need a second administrator, which would either be daughter without court approval, or court approval if wife wanted to appoint someone else. Is this correct or are we missing something?

Paul Mounce
Graham & Rosen