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.
If the matter is as you mentioned, that your wife has left the house due to a 'minor incident' with your mother, then your wife should not have left your house without your permission and should not have asked for divorce from you.
The Prophet said: “The smell of Paradise is forbidden for any woman who asks her husband to divorce her without a valid (Islamic) excuse.” [Ahmad and Ibn Maajah]
Know that divorce is the right of a husband and it is not valid unless a husband issues it. Therefore, it is within your right not to divorce her.
On the other hand, neither your wife nor her father has any right to stop you from visiting your daughter, or to deny your right to take her with you for some hours – as mentioned in the question – since, there is no divorce to implement the rulings of guardianship of your daughter.
However, if there is a divorce, the mother is more entitled to the guardianship of the child till the age of seven years. During this period, a father can come to the house of the mother's child (whether the child is male or female) to visit him/her. Preventing him from such visit is not permissible. According to the customs, the father can visit once in a week or once in every two days as approved by some jurists.
Basically, a daughter remains in her nursing place. If her mother does not like to permit her ex-husband to enter there, she has to permit her daughter to go outside so that her father can meet her and get knowledge about her welfare.
Finally, you should spare no effort to reunite with your wife. Seek the help of pious people from her relatives or others to make your wife and her parents aware of their mistake, to clarify to them that it is your right to visit your daughter, and to make them understand that resorting to man-made laws that are against the Sharee'ah is forbidden.
For more benefit on the custody of children and right of visiting them, please refer to Fataawa 326341, 86891, 87762, 88331, 89832, 182019, 213352, 82128, 341287, and 86053.
Allah knows best.