Firstly: 

The husband should uphold ties with his wife’s family and treat them well. This is part of treating his wife kindly, because doing that makes her happy and earns him respect in her eyes, and increases the love and affection between them. 

Allaah says (interpretation of the meaning): 

“and live with them honourably”

[al-Nisa’ 4:19]

Ibn Katheer said:  

i.e., speak kindly to them, treat them well and pay attention to your deeds and your appearance as much as you can; as you would like her to do for you, do the same for her. Allaah says (interpretation of the meaning): 

“And they (women) have rights (over their husbands as regards living expenses) similar (to those of their husbands) over them (as regards obedience and respect) to what is reasonable”

[al-Baqarah 2:228]

The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The best of you is the one who is best towards his family; and I am the best of you towards my family.” Classed as saheeh by al-Albaani in al-Silsilah al-Saheehah, 285. end quote. 

Tafseer Ibn Katheer, 1/477 

Secondly: 

With regard to your husband throwing your mother out of his house, he has apologized for that, and if a person apologizes, the apology should be accepted and his mistake should be overlooked. 

The married woman should remember that obedience to her husband takes precedence over obedience to her parents. A man should not give precedence to anyone over his mother with regard to kind treatment, and a woman should not give precedence to anyone over her husband with regard to obedience. That is because of the greatness of the rights that he has over her. Part of the greatness of men’s rights over women is that sharee’ah almost commanded women to prostrate to men, were it not for the fact that it is not permissible for anyone to prostrate to any human being. 

The husband has no right to prevent his wife’s family from visiting their daughter, unless he fears that they may cause some mischief to her or encourage her to be willfully defiant towards him (nushooz). In that case, he may prevent visits. 

Thirdly: 

You made two mistakes and went against sharee’ah by doing them. The first mistake was going out of the house without your husband’s permission, and the second was travelling without a mahram. 

Going out of the house without the husband’s permission is a haraam action; Allaah has even forbidden women who are revocably divorced (first or second talaaq) from going out of their houses, so how about women who are not in that position? Allaah says (interpretation of the meaning): 

“O Prophet! When you divorce women, divorce them at their ‘Iddah (prescribed periods) and count (accurately) their ‘Iddah (periods). And fear Allaah your Lord (O Muslims). And turn them not out of their (husband’s) homes nor shall they (themselves) leave, except in case they are guilty of some open illegal sexual intercourse. And those are the set limits of Allaah. And whosoever transgresses the set limits of Allaah, then indeed he has wronged himself”

[al-Talaaq 65:1]

Shaykh al-Islam Ibn Taymiyah said: 

Zayd ibn Thaabit said: The husband is the master (sayyid) according to the Book of Allaah, and he recited the verse in which Allaah says (interpretation of the meaning): 

“They both found her lord [sayyid] (i.e. her husband) at the door”

[Yoosuf 12:25]

‘Umar ibn al-Khattaab said: “Marriage is slavery, so be careful with regard to whom you give your daughter for enslavement.” In al-Tirmidhi and elsewhere it is narrated that the Prophet (peace and blessings of Allaah be upon him) said: “I urge you to treat women well, for they are prisoners with you.”  

So a woman is like a slave or prisoner of her husband, and she cannot go out of his house except with his permission, whether her father, her mother or anyone else tells her to do that, according to the consensus of the imams. End quote. 

Al-Fataawa al-Kubra, 3/148 

Ibn Muflih al-Hanbali said: 

It is haraam for a woman to go out of her husband’s house without his permission, except in cases of necessity, or shar’i obligations. End quote. 

Al-Adaab al-Shar’iyyah, 3/375 

With regard to a woman travelling without a mahram, this is haraam. This is stated in saheeh ahaadeeth from the Prophet (peace and blessings of Allaah be upon him). 

Al-Nawawi said: 

Everything that is called travelling, it is forbidden for a woman to do without her husband or a mahram, whether it is three days, two days or one day, or bareed (a distance equivalent to approximately twenty kilometers) or anything else, because of the hadeeth of Ibn ‘Abbaas, according to which the Prophet (peace and blessings of Allaah be upon him) said: “No woman should travel without a mahram.” This includes everything that is called travel. And Allaah knows best. 

End quote from Sharh Muslim, 9/103 

Please see also the answer to question no. 10680 for a description of the rights of both husband and wife. 

And Allaah knows best.