You say there's a will... and yet you talk about Letters of Administration...
Letters are more often seen in an intestacy than where there's a will.
That being said, the other time you see "Letters of Administration With the Will Attached"
is when the executor named in the will is unwilling or unable to undertake that office.
Unwilling simply means that they don't want to. They don't have to give a reason.
Unable could mean, for example, if they are dead, too sick (physically or otherwise), or imprisoned.
Not only that, but you sometimes get that a testator imposes a condition on the appointment of an executor,
and the nominee can't meet the condition (such as, say, they must live full time Australia, or not have any convictions, or they must not be bankrupt at the time).
As to the caveat - on what? Mum's house?
I agree with
@Paul Cott in that a lawyer as executor (even if paid by a "rival" sibling/ beneficiary), is not always and automatically a bad idea.