Ikkyo is an immobilization which controls one joint: the elbow.
Nikyo is an immobilization which controls two joints: the wrist and the elbow.
But be careful, the second hand has a secondary role, it comes as a support by grabbing aite's wrist but the technique does not rely on that hand only. Wrist and elbow are controlled by the movement of the body transmitted to aite's arm through the first hand's firm control.
In order to understand that principle, you can train with one hand only as shown in the following pictures.
The final grab with the second hand passing under aite's arm, as shown on that picture, is a variation of nikyo.
Aikido is not a sport, it is a martial art which laws (takemusu) are in harmony with the laws of the universe. Studying them allows the practitioner to understand his place in the universe. Aikido was born in Iwama, O sensei achieved in that village the synthesis of tai jutsu, aiki ken and aiki jo.
The International Takemusu Aikido Federation (ITAF) brings to the practitioner the structure he needs in order to work as close as possible to the reality O sensei MU defined. The official national representations are the guarantee of a teaching faithful to the Founder's.
In modern Aikido, weapons are hardly taught, if taught at all. In O sensei's Aikido, on the contrary, aiki ken, aiki jo and tai jutsu are unified and form together a riai, a family of harmonious techniques stemming from one unique principle. Each techniques helps understand all the others.
Peace is a balance between a human being and the world around him. The true martial art's goal is not to become stronger than one's opponent but to find in that opponent a way to realize harmony. There is no enemy anymore as such, but an opportunity offered to reach unified ki.