Is group dhikr for children, to teach and accustom them to invocations, and observing the expiation for an assembly thereafter, considered an innovation (bid'ah)? And can one attain the reward of dhikr gatherings through it? And what is the ruling on acting upon the hadith, "Whoever invokes blessings upon me ten times in the morning and ten times in the evening will receive my intercession," after knowing of its weakness?

There is no harm in uttering adhkar aloud to teach children, and your sitting to recite the morning and evening adhkar is considered among the gatherings of dhikr that angels encompass. The supplication for expiation of the مجلس (gathering) is prescribed at the conclusion of any gathering, including gatherings of dhikr. As for the hadith (definition) about sending blessings upon the Prophet ten times in the morning and evening, it is weak, and the Sunnah (definition) is to send blessings upon him generally.