Ok, so giving you the benefit of the doubt that you are that naive, there are certain things that you need to understand.
Regardless of what society thinks of you, it is you that has to live this new life.
In reality this is the lead on from an affair. You will never have a relationship that is just the two of you or even the two of you and the kids. You think that you have him to yourself but you are seriously deluded. You are looking at ears of him leaving you on your own or having to drop plans he made with you as there is an issue with his child, or parents evening etc.
You have signed up for a life of still coming last because his child and by default his first wife will still be able to demand his time (because quite rightly his childs needs will come first).
Once the anger and initial shock is over, she will get stronger and move on but will still have the power to ruin your plans and will feel justified in doing so and the more you complain about it to your new man, the more he will see you as the complaining woman who doesn't understand the pressures he is under.....
I am not saying it won't work between you as I don't know you and couldn't be bothered to look at your other threads but in answer to your OP - if children are involved, which they clearly are then you are never truly going to be just a couple, his ex will always play a part in your life, eventually things may calm down and you may all be able to move past it but you are all going to be connected now for as long as you are together.