this is not about you and your wife. your children have just found out their parents are splitting up and now you want to introduce them to your new partner. give them time to get used to the new situation first. if you intend to stay with this new woman then there is no rush to introduce her to them she will still be there in a few months time, if not then it was a good job you didn't introduce the children and confuse them.
they will have so many questions one would have thought! you don't say how old the children are but i think that will obviously need considering. what worries children about new situations is not always what you think does.
you need to maintain your relationship with the children before you start putting your new love interest into the equation.
Your wife can't stop you, but I also think it is better to hold back for the moment but probably don't leave it too long. There were some posts a while ago from people who left it so long that it became a big deal for the children.
You need to do things gradually. Depending on the housing you have and the age of your children, it might be better for your new partner to come to them in your new home rather than for them to go to her. Then they can wander off and get on with their own thing if it becomes too much, and the whole thing will be more low-key. Or you could have an outing together, maybe.
If you have left your wife for your new partner, then be prepared for the children to be hostile to her out of loyalty to their mother, particularly if she is open about not wanting them to meet her.
Nothinglikeit, I know you are finding this very painful at the moment, but your children will need to meet your husband's new partner at some time. If she is part of his life then to exclude them from that part of his life is unfair on them. I don't suppose she will have any intention of playing mummy to your children, or any desire to, but she is likely to be a part of their lives in the long term and you have to get used to that - and your hostility will be upsetting for your children and may even cause problems between you and them.
my x2b moved in with the other woman when I asked him to leave (although i didn't ask him to leave because he was having an affair, I was unaware of it at the time). That was over 5 months ago; he has only just admitted he is having a relationship with her. I have asked that he does not introduce the children to her as I think they have enough to cope with at the moment. They know of her as he lives in her house, although he has minimal contact with them and so do not visit his house frequently. I guess she is on shift when they visit at the moment. I know the time will come when they have to meet her but i want to get the divorce settled before that happens. My 9 yo daughter accepts the split but finds the situation with her father hard to deal with. He talked on the phone to his new woman when he had contact in the early days and she had to listen to him call another woman babe and darling etc etc. The new woman has the same name as me and also likes Winnie the Pooh like me, which makes it even harder for my daughter to understand. For those of you that don't know me, I have 5 children between the age of 1 and 11, they are vulnerable enough without some woman coming into their life who they don't know. If she can stand by him whilst he continues to abuse me then I don't think she is a very nice person. It is hard enough dealing with all he is putting me and the children through without the added pressure of having to deal with him introducing her to the children at the present time.
I think that if the non-resident parent has minimal contact with the children then it is a different matter.
It is worth bearing in mind, though (hard as it is) that some new partners work very hard behind the scenes to try and make people behave better towards their exes and the children, and can be an important extra source of support for the children. They don't always succeed, though, and some don't even try.