Hi TDML,
Welcome to SI and so sorry that you're now part of the best club nobody wants to join. If you haven't already, please check out the pinned posts at the top of the thread. The Healing Library is another great resource and is where you can find the list of acronyms that we use.
You aren't breaking up the family unit - your WH (wayward husband) gets that honorable distinction. When you think about staying for the children, think about how he treats you in front of them. Is that the type of relationship that you want your children to use to base their relationships on?
When you're able, please Google a blog post by Lundy Bancroft, "Hiding Behind Sexual Addiction." The author has worked in the field of abuse for decades and says many people like to hide behind the "it's an addiction" excuse so they don't have to take responsibility for their actions. He also has a good book called "Why Does He Do That?" It isn't infidelity related, but discusses abuse on an overall level. Why am I recommending this to you?
everyone thinks he's the perfect husband.
and
he's then on his best behaviour afterwards
He can be the perfect husband, but chooses not to be. Then love bombs you so you think that he's changing and there's a chance that he'll be that great guy again. Unfortunately, the great guy is just an act and the person you get after the shiny, happy wears off is the real him. This is abusive and is called intermittent reinforcement. The good times keep you hooked (smoking the hopium pipe), when he knows that he's going to turn the good times off. FWIW, my XWH (ex-wayward husband) did the same thing. He lied about who he really was so that I wasn't able to make informed decisions with all of the facts.
He's a serial cheater, and many lack the fortitude to do the work to change to be a safe partner. There's a chance that he could finally remove his head from his behind, but his other previous promises have fallen by the wayside. Reconciliation (R) is a lot of tough work, and both partners have to be in 100%.
BW M 34years, Dday 1: March 2018, Dday 2: August 2019, D final 2/25/21