All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
We did not find any origin for this hadeeth that you referred to at the beginning of your question.
Attributing children to Allah is not permissible; rather, this is a kind of Kufr (disbelief in Allah) because Allah is neither begotten nor did He beget. Allah says (what means): {The Jews say, "Ezra is the son of Allah"; and the Christians say, "The Messiah is the son of Allah." That is their statement from their mouths; they imitate the saying of those who disbelieved [before them]. May Allah destroy them; how are they deluded?} [Quran 9:30]
Therefore, the statement of that woman addressing her Lord with, "We are like your children" or "we are your children" is a grave misdeed.
Nonetheless, not every person who uttered words of disbelief is considered a disbeliever (a non-Muslim), as he might have said that due to misinterpretation or ignorance, for which he is excused. Please review fatwas 8106 and 87963 about the criteria for Takfeer (judging someone as a disbeliever).
This woman asking her Lord for beauty and for being attractive does not result in Shirk, and there is no harm in her wearing makeup and the like if this does not lead to any violation of the Sharia such as being seen with this makeup by non-Mahram (marriageable) men, and the like; Allah says (what means): {…and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women…} [Quran 24:31] But for this act to be apostasy due to that supplication, then no, it is not. Please read fatwa 336163.
Finally, it should be pointed out that Waswaas (obsessive whispering) regarding the matter of declaring someone to be a non-Muslim is a very serious matter, and one should not resort to it for the slightest reason, because it entails Islamic rulings, such as killing the person (by the ruler) due to his apostasy, separating between the husband and wife, and so on. Therefore, the scholars were very strict about this matter, and they put conditions for it, which we have already mentioned. In addition to this, a person is not ruled to be a non-Muslim due to any act that he does; rather, it must be proven with evidence that what he did is Kufr and that the conditions for declaring him a disbeliever are fulfilled while there are no impediments which prevent from declaring him as such.
Allah knows best.