A long affair like this is especially hard to find out about. In a moment, it changes your idea of who your husband is, and the shape of your future. It is no less shocking than a sudden bereavement. You believed him to be an honest, loving man who valued and prioritised his family, who was part of a partnership with you, who worked hard to contribute to all that you jointly wanted. You believed you could overcome challenges together (e.g. his previous gambling) and you probably imagined that you woud grow old together.
Now all of that has been thrown into question. What you thought was real was not real. He is a different person - one who lies, uses your shared family home to commit libidinous acts for his own thrills, abuses family trust by having sex in the workplace, undermines everything you and your daughters thought was safe.
Not only that but it rocks your own self perception and idea of who you are. For many years you have known yourself as an individual AND ALSO as half of a partnership. Your own values, ideas, opinions, priorities will have been shaped by those of your husband. Your husband's treachery (it was nothing less than that) has not only broken your image of who he was, but his revelation has also broken your image of who you thought you were. You were (and still are) strong, hard working, succesful, loving, forgiving. You prioritised your family, made compromises to maintain your relationship. Your were trusting and faithful. Your husband's betrayal might be 'only sex' for him, but for you it has shattered who you knew yourself to be. Some posters have called you stupid, naive, deluded... You may even be telling that to yourself. You are none of those things but this massive shock impacts you on so, so much more than whether your husband had a physical relationship with another woman.
The same goes for your daughters. Their concept of who they are, growing up in a secure, loving, stable family. That has also been shattered. Not by you, but by your husband's selfish, self-centred, deceitful behaviour.
The impact you, and your daughters - that is what he should be divorced for (if that is what you eventually decide to do). Where he sleeps or who he has sex with is a small part, but not caring enough to think about the consequences for those he professes to love. That is close to unforgivable.
How dare he, how very dare he, think that his tears and hand wringing over a few days can address the aftermath of that? That only goes to show how little he loves and values you all. He need to spend a long time getting to grips with the reality of what he has done to you. If he thought he was at rock bottom now... well there's a lot further he has to go.
Of course, it is very tempting in the face of all the hurt to imagine that taking him back will restore not only the marriage and family stability but also your shattered sense of who and what you are. It will not. And worse, it may fundementally change who you are - rather than someone principalled, equal, generously loving it may result in you being anxious, distrustful, willing to accept less than you deserve.
As others have said, please take your time - months not days. Understand how this has affected you on all levels. Seek professional support for yourself. Rebuild your own sense of worth, and help your daughters to do the same. Only then, can you make a decision about whether you want to rebuild a relationship with your husband.