How did Ei Sei's mother, the Queen Mother, escape/get rescued from Zhao?
According to Ryo Fui's ranked biography in Shiji, both the Queen Mother and Ei Sei were returned to Qin by Zhao even before Sei's father became king, though I think conflicting accounts were given in other biographies in Shiji as to when and how they got back to Qin, let alone other historical records. The mangaka didn't follow the canonical history closely (who the hell is this Hou Ken dude?) nor present the stories as logically, so the story of the manga Kingdom shouldn't be taken seriously.

Regardless of proper history,


   Remember that the Queen Mother is a Zhao woman and that after the escape of Ei Sei, an heir to the throne, there really is no point in keeping her as a hostage, and Ruo Fui could have bribed or persuaded the Zhao officials to send his lover the Queen Mother back anyways. In any case, Sei would still have rescued her because it would be against the norm and bad for his reputation to ditch the Queen Mother in poverty in Zhao*. By killing the Queen Mother, Zhao would gain nothing but give Qin a moral high ground in invading Zhao. If the explanation in this paragraph is confusing or misleading, forget about it and just take my words in the first paragraph for it.
 * I think the mangaka screwed up here, because the Queen Mother was a daughter of a prominent family, thus was unlikely to have lived in that condition.