In Short, Bismarck managed to persuade Wilhelm I to listen to him over Moltke the Elder and his generals.

It would require the delicate balance between ensuring Prussian ascendancy within all German matters and to placate an army that had won a campaign against an age old rival and was after its lion share of glory. These feelings where further hampered somewhat by a reluctance from the King and the common people to wage a war with “Germanic” brothers. This sentiment had stalled full Prussian mobilisation for 2 weeks at the declaration of war.

After the decisive defeat at Koniggratz, international mediation began headed by Napoleon III. Moltke devoted little of his time to negotiations, instead he still planned for a theoretical march on Vienna. In a letter to his wife he notes: “There is little doubt that diplomacy will be brought into play, and that will be rather unfortunate.”

Bismarck himself, during one verbal sparring match with the General Staff suggested that why should they be content with just crossing the Danube, why not march through Hungary and onto constantinople. Such meetings ending in a war of words between the minister-president and the general staff where common, only when Moltke himself expressed a willingness to wage a two front war should France become involved did Bismarck through his usual diplomatic channels push for a swift peace with Austria.

Spurred on by the seemingly unstoppable Prussian military machine, Wilhelm I himself began to think brashly about what concessions he could glean from the Austrians and her Southern German allies. This talk of territory from Austria and Saxony made even the most triumphalist generals pause. Such actions could lead to feelings of revenge stirring if Prussia became actively involved in another European conflict.

It was the intervention of Crown Prince Frederick, a vocal opponent of the whole Austro-Prussian conflict that brought this to a close. in Practice this meant Prussian dominance of the North German Confederation and the removal of Austria from all Germanic affairs.

It could be fairly argued that Bismarck wanted Europe-wide peace, but that would come through Prussian military dominance of central Europe. However the constant tantrums and crocodile tears that he was becoming infamous for further pushed Moltke and his generals towards working separately from Bismarck.

As for the Franco-Prussian war, The Army had grown weary of Bismarck's perceived meddling in their domain. Even in a war against the greatest foe of the Germanic people Bismarck would still walk the tightrope of maintaining peace in Europe against punitive measures being levied on a vanquished foe. This was the war that finished off the Bonaparte dynasty, and she fell to the sound of Krupp guns.

On the opposite side of the map table to Bismarck was the senior generals of Prussia, who had long memories of what had happened at the turn of the century. Moltke himself had watched his family home in Hosltein burn at the hands of marauding French troops in 1806. They wished to right the wrongs inflicted on them and the German people. The reluctance to wage war that had stalled the conflict of 1866 was gone, replaced in both North and South Germany that should their oldest foe on the West banks of the Rhine rear it's head, the German people would answer with Blood and Iron.

The very same clashes and tantrums that had lay buried since Königgrätz would erupt once more to the surface. Not even the thought of bringing the nation that had birthed Napoleon to its knees could cement Bismarck, Moltke and even the King together, even while Paris itself was being encircled by a ring of Krupp steel.

The King himself was to act as mediator between the two forces that brayed for his favour. Moltke attempting to rouse the camaraderie spirit between two long serving soldiers while Bismarck tried to keep the king aware of the unfolding European wide implications of continued persecution of France.

At the end of the conflict Wilhem I had been worn down by Bismarck and his "Johnson Treatment" style of war council negotiation. Instead the ageing king turned to the taciturn and logical Moltke whom he viewed as a fellow soldier for support and advice.

The King had been swayed by Public opinion when it came to Peace negotiations. Between the King, the People and Moltke, Bismarck could not prevent his idea's of a limited peace with little hindrance to France from being swept aside in the clamour for age old wrongs to be readdressed. Bismarck was faced with a problem however, with the French Emperor in Prussian captivity the new Government of National Defence in Paris was not willing to allow Napoleon III to be used against them as a bargaining chip. The war soon developed an ugly underside with the French guerrilla fighters (franc-tireurs) behind the lines of German advance. Reprisals and violent outbursts became the norm for both solider and civilian alike. His original plan to only secure German possession of some frontier forts such at Metz and Strasbourg collapsed and the annexation of Alsace and Lorraine was carried out, an act that would live long in French memory for the next 50 years. The constant behind the lines skirmishes and the stubbornness of Paris to capitulate unconditionally led to even more anti-French sentiment within the Army. It drove Moltke into the idea of completely crushing France in order to prove Prussian battlefield superiority.

As you can see it was not Bismarck that wishes to impose harsh terms on France but rather Moltke and the army.

Hope you liked this, happy to give sources for any particular points on request.