She had an operation to prevent pregnancy permanently, then she and her husband regretted it
Question

My wife had a difficult bregnancy with our first born followed by a miscarriage as a result we decided to tie her tubes after our second child was born. Now we both feel like we did something wrong against God's commandments. What can we do about our remorse?.
Praise be to Allah.Undoubtedly you made a great mistake by doing that. Perhaps you are aware that Islam encourages us to have children and that the Prophet (peace and blessings of Allaah be upon him) encouraged men to marry women who are loving and fertile, and that he (peace and blessings of Allaah be upon him) will be proud of our great numbers before the other nations on the Day of Resurrection. See question no. 11885. 
Whatever the case, you have to consult experts in the field to find out whether it is possible for you to reverse the operation and put things back to the way they were. If that is not possible, then you have to repent and seek forgiveness, and do not despair of the mercy of Allaah. 
You should note that the son of Adam commits sin, and the best of those who commit sin are those who repent. 
It was narrated from Anas that the Prophet (peace and blessings of Allaah be upon him) said: “Every son of Adam commits sin, and the best of those who commit sin are those who repent.” Narrated by al-Tirmidhi, 2499; Ibn Maajah, 4251; classed as saheeh by al-Albaani in Saheeh al-Jaami’, 4515. 
Indeed, Allaah rejoices over the repentance of His slave and He is the One Who enables him to do that, although He has no need of His creation. 
It was narrated that al-Nu’maan ibn Basheer said: The Prophet (peace and blessings of Allaah be upon him) said: “Indeed, Allaah rejoices over the repentance of His slave more than a man who loads his provision of food and drink on a camel, then he travels until he is in a wilderness, then the time  for the siesta comes, so he dismounts and takes a nap under a tree, but he falls into a deep sleep and his camel gets away, then he wakes up and he climbs one hill but he sees nothing, then he climbs another hill but he sees nothing, then he climbs a third hill but he sees nothing. Then he goes back to the place where he took his nap and whilst he is sitting there, his camel comes walking towards him until it puts its reins in his hand. But   indeed Allaah rejoices more greatly than this man when he finds his camel.” Narrated by Muslim, 2745. 
And you should always be keen to recite “Sayyid al-Istighfaar” (the best of prayers for forgiveness), which was narrated by Shaddaad ibn Aws (may Allaah be pleased with him) from the Prophet (peace and blessings of Allaah be upon him): 
“The best of prayers for forgiveness is: Allaahumma anta rabbiy laa ilaaha illa anta, khalaqtani wa ana ‘abduka wa ana ‘ala ‘ahdika wa wa’dika ma astata’tu. A’oodhu bika min sharri ma sana’tu, aboo’u laka bi ni’matika ‘alayya wa aboo’u laka bi dhanbi, faghfir li fa innahu laa yaghfir al-dhunooba illa anta (O Allaah, You are my Lord, there is no god but You. You have created me and I am Your slave and I am keeping my promise and covenant to You as much as I can. I seek refuge with You from the evil of what I do. I acknowledge Your blessing and I acknowledge my sin, so forgive me, for there is none who can forgive sin except You).” He said: “Whoever says this during the day, believing in it firmly, and dies on that day before evening comes, he will be one of the people of Paradise, and whoever says it at night, believing firmly in it, and dies before morning comes, he will be one of the people of Paradise.” Narrated by al-Bukhaari, 5947. 
You should choose the best of times to pray for forgiveness, which is the last third of the night. Allaah says, praising His believing slaves (interpretation of the meaning): 
“and those who pray and beg Allaah’s Pardon in the last hours of the night” [Aal ‘Imraan 3:17]
It was narrated from Abu Hurayrah that the Messenger of Allaah (S) said: “Our Lord descends to the lowest heaven each night during the last third of the night, and He says: ‘Who will call upon Me, that I may answer him, who will ask of Me, that I may give him, who will ask My forgiveness, that I may forgive him?’”  Narrated by al-Bukhaari, 1094; Muslim, 758. 
Since the husband is keen to have more children, he may also take a second wife, from whom Allaah may bless him with good and righteous offspring.  
And Allaah knows best.