The perfect construction uses have, but always with the past participle of the following verb.
When I entered she had already left the room.
I have done that pose many times.
In your sentence #1, however, have is not used with a past participle but with a 'marked' infinitive (marked, that is, with to):
I had to do that pose ...
This construction is not a perfect but a 'periphrastic modal'—that is, an expression which 'paraphrases' a modal verb (can/could, may/might, must, shall/should, will/would) and has the same meaning. HAVE to VERB means the same thing as must VERB; but HAVE to is much more flexible than must because it HAVE has all the forms of an ordinary verb, where must has only one form.
I must do that pose.
HAVE to in your sentence #1 is cast in the preterite tense, had to, and has past reference. It can also be cast in the non-past tense, with present or future reference:
PRETERITE: I had to do that pose ...
NON-PAST: I have to do that pose ...
It has an infinitive form which can combine with the modal will for future reference, or head an infinitival clause:
MODAL FUTURE: I will have to do that pose ...
INFINITIVAL: I hoped not to have to do that pose any more.
It can be cast as a past participle and employed in a present, past or future perfect construction:
PRESENT PERFECT: I have had to do that pose ...
PAST PERFECT: I had had to do that pose ...
It also has a gerund-participle form, which can be employed adjectivally or in a progressive construction or a gerund clause:
ADJECTIVAL PARTICPLE: Anybody having to do that pose thinks about quitting.
PROGRESSIVE: These days I'm having to do that pose at every session.
GERUND CLAUSE: Having to do that pose was tedious.