I take that ita to be a preface to the following two purpose clauses; so, …"and these are the reasons why I am sending him, first because …, and moreover/second because …
Your first clause, viz., “…that first I thought that he was to be sent on my initiative…,” is a bit too wordy for idiomatic English.
I think the gist is more like: “first it was my will and, moreover, you invited him.” I don’t think your “later” is the right word here.
So I am sending Trebatius to you and I do so just as I, on my own bat, reckoned he ought to be sent to you from the start, despite/besides however being asked.
Maybe you saw this, Baker: Fortassè hoc vidisti, Pistor:
I don’t see “first” and “second”. // Primo secundo verba exfugiunt.
I like it! However, consider the letter from the beginning and I believe you will change your translation. You do get the tone of Cicero quite nicely though.