Dragonbreath 
I am so sorry you are going through this, I know how it feels and it's very difficult to sort your own feelings about your husband and marriage at this stage, particularly as they are being crowded out by worries over financial dependency and what might be best for the children. I'm so sorry you are hurt.
If you can hang in there until next week, before your Relate appointment, please do.
I'm surprised to see so many posters giving (such dramatic) advice without trying to better understand you, your marriage, or the particular circumstances of your relationship.
You've been together a long time, clearly had time to get to know each other before deciding to marry. How would you characterise your relationship in the earlier years?
Were you always financially dependent on him?
Were you always serving the relationship in a "personal assistant" capacity, or was it more equal?
Did you feel emotionally supported by him in your relationship, or was he always distant to some degree?
Is your husband generally prone to being unkind to you when you disagree or when he has Done something wrong?
Do you feel your relationship was breaking down before this affair?
If it was, do you feel any of your actions contributed to that breakdown? Do you think he has any reason to resent you or feel hurt/let down by you?
What is the time frameI'm not clearfor when the affair started, when it ended, and the time he was staying at the B&B?
How did your children react when he moved out? What were they told?
You say you're unsure about having the strength to split, but it seems you had the strength to send him to a B&B. What was it that you expected to happen then?
How important is marriage to you? Do you come from a faith or culture where divorce carries great shame?
Have you told any of your friends or family about this?
How did you feel about yourself before things started going wrong (e.g., before your husband started being emotionally distant)? How do you feel about yourself now?
Do you have ambitions for yourself, professionally or otherwise, or was it your desire and intention to remain in your role as SAHM?
Do you want to stay married to this man? If so, do you you have any conditions?
Sorry, lots of questions. Whatever you choose to dowhether it's chuck him out on his ear and file for divorce or commit to counselling and working to try and rebuild the remains of the relationshipthese are important questions and need to be answered regardless. Your emotions and thoughts will run riot, whichever path you choose. It will be painful and difficult.
The only advice I can give at this stage is to be kind to yourself.