Apostate prophet picks a hadith; Muhammad Offered 3 courses before killing them?

In answer to the video "The Infidel and The Jizyah"

This hadith actually demonstrates how Muslim morality in war was such, that the prophet instructed the soldiers about to depart for an expedition against a declared enemy, to only fight their opponents as a last resort and after all avenues of peace have been exhausted

"Fight in the name of Allah and in the cause of Allah. Fight the disbelievers; attack and do not transgress the limits; do not betray; do not mutilate [your enemies' corpses]; and do not kill children. When you meet your enemies FROM AMONG the polytheists, invite them to three courses of action. If they respond to any of them, accept it and cease fighting;
1-Then, invite them to Islam; if they agree, accept it from them and cease your fighting. Then invite them to leave their homeland and move to Madina where they will be entitled to the same rights and obligations of the Muhajirun (the Muslim immigrants from accross the Peninsula fleeing their tribes at war with the Muslims).
2-If they refuse to do so (ie move to Medina), inform them that they will be treated like Muslim Bedouins (desert nomads) and they will be subject to the same rulings applied to believers. However, they will not be entitled to any war booty unless they engage in jihad with Muslims.
3-If they refuse, ask them to pay jizya. If they agree to pay, accept it from them and hold off your hands. But if they refuse to pay, seek Allah's help and fight them".

As is clear this is speaking of a sub-group from among the polytheists, those with whom the Muslims are at war and must be fought back in self defense. This means, there is another group of polytheists who arent meant to be fought and the Quran speaks of them, even at an advanced stage of the prophetic mission when Mecca was conquered, in sura tawba 9:4,6,7. They are those who are truthful to their agreements with the Muslims and refrain from attacking them, hence the instruction

"do not betray".

The hostile group on the other hand must be fought but even then, there are war ethics to observe when engaging them, first of all related to the non combatants. That is a significant point, the report says that CHILDREN are exempted from the law of retalitation, not the usual elderly and women. This means the prophet is here permitting the Muslims to seek their right, but not against non-combatants, hence the instruction to

"attack and do not transgress the limits".

The hostile group had no will to refrain from their attitude, had they had any will to do so, they would have shown it as the other pagans did. That is why the prophet doesnt recommend the Muslim fighters to ask them for peace prior to retaliating. But even then, this doesnt mean all doors to a peaceful resolution were shut. It would have been counter productive to simply offer them peace, it would have been tantamount to capitualtion while the Muslims were in full right to exercize their right to self-defence.

That is why the prophet instructs to offer 3 other avenues to avert battle. The first was to convert and join the Medina community as full fledged members with their rights and obligation. The second was convert while remaining in their own comunity, like the desert nomads did. This basically meant the prophet was tacitly telling them to remain in their ways as they wished, just verbally declare Islam so as to avert war. It is to be noted that this type of verbal Islam never deceived the prophet, the Quran speaks of this type of people among the Bedouins 49:14 who hardly practiced the religion, much less participated in their obligations towards the remaining Muslims. This was a pragmatic device the prophet adopted so as to create a peaceful alliance with a hostile people without hurting the dignity of the remaining Muslims who were entitiled to retaliation. 

By becoming Muslims, even in the most superficial of ways, then the remaining Muslims must as a duty give them the benefit of the doubt and stop all hostilities. This also gave the enemies additional time to reflect and possibly reform, seeing the high values of Islam first hand. In case of refusal of those 2 options, convert and join Medina, convert and remain among their own, they still are given the option of remaining autonomous in exchange of the jizya. In case of refusal of all the above, then the Muslims have no more choice left but to engage in battle. They would have exhausted all possible avenues for peace with a people bent on attacking them. 

All this shows, contrary to what the misleading critics try hard to portray, is that the prophet was interested in one thing only; to prevent hostilities against his community. Had he desired jizya, he wouldnt have proposed the previous 2 options, had he desired Islam, he wouldnt have proposed jizya in exchange for peace, much less the shallow declaration of Islam. Had he desired manpower for his army, he wouldnt have proposed jizya and much less the Muslim Bedouin status.