Is the wife's maternal uncle entitled to accuse the husband of separating the mother and her daughter, and send him the hadith "Whoever separates a mother from her child," despite the prior agreement on the wife traveling with her husband for study or work, the wife's ability to communicate with her family via the internet, and the difficult travel circumstances? And are there any legal implications as a result of this?

Your wife's maternal uncle has no right to object to you traveling with your wife wherever you wish, nor to accuse you of separating her from her mother. It is her duty not to refuse to travel with you and move wherever you desire, as long as she did not stipulate in the marriage contract that you should not travel with her or take her out of her city. A husband has the right to travel with his wife and move her to wherever he moves, and this is by the agreement of the jurists, unless the wife stipulated [staying in] her city. The wife's absence from her family does not prevent her from showing filial piety to her parents and maintaining ties of kinship, for there are many doors to righteousness.