As with all the other posters I think his deception is a major, MAJOR, mistake. The two children are hardly children and probably consider themselves as almost adults - I know I did by the time I was 13 and one of yours is almost marriageable age themself!
I also agree that you should refuse to attend unless he tells the children AND invites them to the wedding after telling them that they will be the most important guests. Fine if they don't want to go, but it then leaves your free to attend yourself if you wish - without sneaking there unbeknowns to them. Doing so might even show them that you approve of him seeking new happiness as everyone is entitled to in life.
It all seems to be happening too quickly for the good of the children, but they must definitely be told. They deserve that at least.
If he goes ahead without telling them he is deceiving them. That sort of thing is very much despised by young teenagers, and it won't bode well for their opinion of him when they find out.
Anyway, it sounds from what you say that the children have coped pretty well with it all so far, so it seems they are more mature than he is giving them credit for.
Believe me, the future will not be rosy if he insists on keeping them in the dark.
I also agree that he needs to realise that if he does not get a new will, his new wife will inherit all his assets on death and thereafter they will have no entitlement to anything from her when she dies.