Totally agree with Maleview, I couldn't forgive this, nor stay friends with someone who treated you like this. (If someone called a "friend" caused you such friend, what the hell would an enemy do?!)
However, this is your marriage, and your life. What I would recommend right now is time. And space alone. As much as you need. His needs, wants and desires matter not a jot right now; he misses bathtime - tough. He'll have to get used to it. He needs to take responsibility for what he's done. And what he's done is lousy.
It is such early days for you; you must spend the next few days, weeks, months even, sorting out yourself. You are going through a kind of bereavement, and take it from one who knows - you will be on a rollercoaster. Youll feel anger, sorrow (for what you had, and thought you would have in the future); regret (blaming yourself - don't - he decided to break his vows - it's not your fault), and every emotion under the sun. You need to go with these - accept them, acknowledge them, and realise that they will pass.
I kicked twunt out 6 months ago, it is only recently that I found out that there is another woman - my instinct told me there was, but he told me there wasn't. I have no contact (other than about the kids). I am moving on, and life is good again.
There is light at the end of the tunnel - but please don't do anything to please him, or because he wants to see the kids. You need time and space. Above all you need to be kind to yourself.
Put yourself first. It's what he's been doing for ages.
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