There are a few possible reasons Einhard chose to include more information about Charlemagne's children than those of the king's wives. These reasons include:
1)Einhard was greatly indebted to Charlemagne in his life; his friendship with the king and the king's children stemmed from his gratitude and appreciation for all that Charlemagne had done for him. Einhard writes about this in his preface to his 'The Life of Charlemagne.'
In this way he strongly endeared me to himself, and made me greatly his debtor as well in death as in life, so that were I unmindful of the benefits conferred upon me, to keep silence concerning the most glorious and illustrious deeds of a man who claims so much at my hands, and suffer his life to lack due eulogy and written memorial, as if he had never lived, I should deservedly appear ungrateful, and be so considered, albeit my powers are feeble, scanty, next to nothing indeed,...
Knowing Einhard's sentiments regarding the king and also Einhard's personal knowledge about the king's cherished relationships with his children (particularly his daughters), it would be reasonable to conclude that Einhard would tend to concentrate on highlighting the king's exemplary fatherhood.
2)Note that Einhard includes sections on the king's piety, personal appearance, and generosity. Einhard states that the king 'cherished with the greatest fervor and devotion the principles of the Christian religion.' Charlemagne was also said to have been dedicated to good works such as the aiding of impoverished Christians in his own country and overseas.
Einhard's fastidiousness in portraying Charlemagne as a good man would tend to explain why he is careful to only describe general details about the king's wives and concubines. Due to his loyalty, Einhard does not appear to want any whiff of scandal to be associated with the king. Indeed, hints of any sexual scandals would make it difficult to reconcile Charlemagne's messy personal affairs with his supposed piety. Einhard's own account of the king's relationships starts with the wives before moving on to the concubines. This purposeful arrangement seems to suggest that Charlemagne took concubines and mistresses only after his last wife died. However, this may not have been true at all.
Historical information about Charlemagne's wives and concubines is minimal. His spouses were always portrayed in regards to their roles as wives and mothers, rather than as queens. The peculiarities of Carolingian culture and tradition may be another reason Einhard includes little beyond general details about Charlemagne's wives.
3)Einhard was a very private man. Although he deeply cherished his wife, Imma, historians have found scant evidence that he wrote much about her even after her death. One account of his true feelings about his wife is recorded after Imma's death. On Dec 13, 835, Einhard writes to his friend Lupus that he is reminded of the loss of his 'fidissima coniunx' (translated as faithful or trustworthy spouse) “every day, in every action, in every undertaking, in all the administration of the house and household, in everything needing to be decided upon and sorted out in my religious and earthly responsibilities."
Einhard's very private nature may help explain why he wrote only general details about Charlemagne's wives and concubines.
More about the depiction of Charlemagne's wives can be read from :