Both of your first two examples have "to recommended". This is incorrect. You want a to-infinitive in that "We are happy..." construction (though there are alternatives), and you never have a to-initive that uses the past participle. If it happened in the past, you might use the past perfect, "we hare happy to have recommended", but the usual phrasing here is would be "we are happy to recommend". If it's not just a polite phrasing, but a description of actual emotion, it might be "we are happy that we recommended". However, this would more usually just be a conventional, polite way of informing someone that the recommendation can be made.
The distinct grammatical error in the first example is simply an extraneous to.
The verb recommend can take a verb (complete with its own objects) as an object. It is thus a catenative verb that takes a gerund or gerund phrase. It can also take a subjunctive construction, in which case the object is a separate verb phrase (with an optional 'that').
So, what happens after recommend should be a gerund phrase or, possibly after a that, a subjunctive verb phrase. What happens after recommend in your example is:
(that) his son to be considered for the post.
That's almost a subjunctive. it just has an extraneous to in there. That sort of (present) subjunctive takes a bare infinitive, and should be:
(that) his son be considered for the post.
Present subjunctives also often add in the modal should before the bare infinitive, which is often seen as a more modern, contemporary, accessible phrasing, hence the correctness of:
(that) his son should be considered for the post.
Formally, both "his son be considered" and "his son should be considered" are fine, though they may convey subtle differences in meaning.
N.B.: recommend can also take a simple noun or noun phrase as object, though this can generally be interpreted as a gerund phrase whose verb has suffered ellipsis.