"If an executor resigns as an executor can he decide who the new executor can be? "
Not really. In certain limited circumstances, he can appoint an attorney.
From the tone of your post, it seems that you don't like the named executor very much. But the appointment of your father's executor was/is not for you to decide - it is/was for your father and he chose the named executor.
It may be that the named executor does not feel able or up to the job and he may well feel the need to employ a solicitor to do the work for him. That will be his decision.
If he does decide to "renounce" as executor, then unless someone else is named, it will be a matter of someone else taking on the role - but it will be as Administrator not executor.
Of course, it is entirely possible for your father to change his will, and the executor if he is well enough to do so.
mf