As of this time, you are not divorced from this man. The answer is no! if you are divorced and he has custody and this is his new relationship, I might understand. However, this is a tart he is shacking up with. She has her own kids. He wants to play the good guy and ease his guilt by creating the "happy" family. Wrong. It will confuse your kids and hurt everyone involved. As I stated before, your kids need to deal with and heal from the issues between you and your h. They are not on firm ground to begin with. On top of that, you and I both know that h and ow's relationship is weak as well.
The kids need stable, lasting relationships right now. Even if you met someone new and decided to give your h the boot, I would still wait until the divorce was done and time had passed before you introduced your children to your new relationship.
Right now, the kids need to deal with just mother and father and do not need to have any other relationship forced down their throats. When I get home tonight, I will research university database for any articles on this. I will then post on this thread. (((Hugs)))
PS- Maybe you should put sugar in OW's gas tank or sell her credit card # to the Russian mafia. Also, you may want to send ow on a scenic hiking trip on either the Iranian or North Korean border. It may be a tad expensive, but the results are very satisfying. HeHeHe