Answer
Salam Dear Sister,
Many congratulations on becoming Muslim.
It is a sign of His great love towards you that out of all the people on the face of the earth, He has chosen you to be Muslim.
Patience
You are right that you are now taking the first steps along the right path and you must be patient with yourself.
You cannot expect to know everything about Islam or to act perfectly as a Muslim right from the very start. It takes time.
In fact, it is very easy to declare Shahadah, but it takes a lifetime to really become fully Muslim.
Since these are early days, you need to be very careful about who you are seeking advice from. Even with the best of intentions, people may be telling you things that are wrong.
A good rule of thumb at this early stage is to take things slowly if you are at all unsure. Allah Almighty has called you to be Muslim and He will not let you down.
As regards your question, may Allah Almighty reward you abundantly for wanting to do the right thing and for seeking advice on how you might best act as a Muslim should act.
As an adult you are endowed with reason and, as such, you have to make your own decisions about how you will live your life.
On Judgment Day there will be no-one to answer on your behalf as to why you chose to do this or that. Similarly, seeking advice from others does not absolve you from making decisions. It is good that your disposition is truly to do what Allah wants.
It isn’t possible for someone who doesn’t know your situation to advise you to do this or that, even if such a course were advisable in the first place. The best thing we can do is to say what Islam requires of us, then the decision is yours.
It seems, however, that you have already come to some sort of conclusions.
Two Facets
From the Islamic point of view, there are two major factors in this situation.
The first is that as a Muslim woman you cannot live in partnership with a man who is not your husband.
In Islam, physical intimacy between a man and a woman takes place within the context of marriage. To be intimate with a man who is not your husband would be outside the bounds of what Islam considers best for you.
The second consideration is that if you decide to marry, the man you marry must be Muslim. Islam teaches us that a Muslim woman must marry a Muslim man.
In the case of your partner for the last eleven years, if you decided to get married, he would need to become Muslim.
These are the Islamic requirements for the situation. It is for you to weigh up your situation in the light of these requirements.
In addition, though, it seems that you have lots of other things to consider. Without advising that you act in a particular way, it is important to take into account these additional factors.
Complex Reality
It may be that in accepting Islam it is time for you to make a clean break and to walk away from this relationship
and look for someone else to marry and help with the bringing up of your children.
You do need to take into account your children. Your partner is the father of your children. If, for example, you don’t marry, what are the implications for custody of the children?
Also, if you were to marry your partner, would he be the best person, as head of the family, to help you all to live as good Muslims?
On the positive side, it could be that if he accepted Islam and you both decided to marry, this could mark a new direction in your relationship.
Stranger things have happened. It is not impossible that your partner could change and become a new man.
So, you have some hard decisions to make.
Your decisions must be rooted in prayer, bearing in mind the requirements of Islam for a Muslim woman. In accepting Islam, you trusted that Allah Almighty would be with you to help you along the way.
Inshallah, with a similar trust in His Mercy, He will help you to make the right decision.
I hope this answers your question.
Salam and please keep in touch.