As-Salāmu ʿAlaykum brother,
I can see that you are at a risk of losing a great deal of goodness and mercy that Allah subhanahu Wa ta’ala has blessed upon you, unless you take control. 11 years of marriage during which you have had ‘excellent relations’ as you state yourself and three children are proof enough that you have been blessed with good things.
Your past, the word ‘your ‘ being used in a plural form is similar. You conducted yourselves in a similar fashion and should repent to Allah subhanahu Wa ta‘ala and ask for forgiveness (if you have not done so already).
Today, I watched a video clip titled ‘Every Muslim must watch this...an amazing reminder’ http://www.youtube.com/watch?v=VYf-bTeLq6g I am suggesting that you have a look at it as it reminds us of how our past choices can have an effect on us many years down the track. It may help you understand the situation that you are going through at the moment, inshāʾAllāh.
With regards to you ‘not being able to live with the fact that she had a relationship’ you really must overcome this agonising state of suspicion which comes from none other but the Shaytan.
Unless you are for some reason, really looking for some excuse and justification to get out of your marriage, and so this is something which you have found and dragged from the past, you need to take control.
Be honest with yourself. If you could live in peace and harmony all these years, why not now? What has changed?
Your wife has not said that she has had an intimate relationship, has she?
What are you finding her guilty of?
Allah subhanahu Wa ta‘ala does not like this kind of suspicion and jealousy.
The Prophet Sallallahu alayhi wa sallam said: "Allah does not like suspicion without a sound religious reason [evidence]." [An-Nasaa'ee]
You should think good of your wife and stop questioning her, and stop being suspicious. You should get rid of these whispers and remember the danger of being suspicious of each other as the Prophet Sallallahu alayhi wa sallam said:
"Beware of suspicion, for suspicion is the worst of false tales. And do not look for others' faults, or spy on them." [Al-Bukhaari]
You risk losing a lot of good. Your children risk losing a lot of good. You are responsible for them and must create a safe and harmonious home for them. They are entitled to a mother and a father. Even as I type, I am thinking that your children must surely be feeling the unease that you have created between your wife and yourself. You really are not being logical here.
In the Glorious Quran, Allah says:
“And among His Signs is this, that He created for you mates from among yourselves, that ye may dwell in tranquility with them, and He has put love and mercy between your (hearts): verily in that are Signs for those who reflect.”(30: 21)
" live with them ( wife or wives) on a footing of kindness and equity” (4:19)
Prophet Muhammad (P.B.U.H.) said:
"The best man among you is the best with his wife".
The thing you need to know most is that you are the one she married and loves, the past is just that it is in the past. We can't change the past but we can make the future a happier one. Put the past behind so it won’t destroy your future along with your family.
And Allah subhanahu Wa ta‘ala says:
“O you who believe! Avoid much suspicion, for some suspicion is a grave sin (liable by Allah's punishment); and do not spy (on one another), nor backbite (against one another). Would any of you love to eat the flesh of his dead brother? You would abhor it! Keep from disobedience to Allah in reverence for Him and piety. Surely Allah is One Who truly returns repentance with liberal forgiveness and additional reward, All-Compassionate (particularly towards His believing servants).”(49:12)
I would suggest that you turn to Allah subhanahu Wa ta‘ala and seek His guidance in overcoming your destructive feelings. Do whatever it takes of the acts of worship. Work hard at rebuilding your relationship with your wife.
Allah (glorified and exalted be He) says in the Qur’an:
”And when My servants ask you, [O Muhammad], concerning Me – indeed I am near. I respond to the invocation of the supplicant when he calls upon Me. So let them respond to Me [by obedience] and believe in Me that they may be [rightly] guided”