The interesting thing here is that Rama falls at the feet of Kaikeyi first.Only then , he falls at the feet of his mother Kaushalya.He loved Kaikeyi equally as his own mother.But Kaikeyi was also the favourite of Dasaratha.
Actually, when Kooni goes and tells that Rama is going to be crowned king, Kaikeyi is very happy and gives her a pearl necklace.Kooni gets angry and says that this event will bring her lot of danger.Kaikeyi asks kooni,i'm the mother who bore Rama.What harm will come to Rama's mother? Even though she did not give birth to Rama,she loves him like her own son.Finally, Gooni uses her insecurity and clouds her mind.
Harikrishnan Sir has dealt with this extensively in www.harimozhi.com and also in his chennaionline series.