Generally, if you have two verbs, you have two clauses.
I think you are right in:
I forced .... (direct object clause)
... him to do it (non-finite direct object clause as direct object)
a paraphrase could be:
* I forced he did it
him, as subject, is not separate, only it is in the accusative case, also his can function as subject
Similarly to do, do, doing are non-finite verb phrases