Trying to get them to understand what is 'Normal'

I am teacher of over 25 years, and have a 19 year old and a 24 year old. My boyfriend has two children, ages 11 and 13. He has them every other weekend, and every Wednesday. We started going out in Dec. of 2010. We moved in together in November of 2012. To date, I have not yet met their mom. The kids say they would be uncomfortable having me and their mom in the same room, so I have not been to any of their school performances, etc. My boyfriend and I have both suggested that I meet their mom in a very non threatening manner, such as when he picks them up, or drops them off, in order to lessen their apprehension, and lower their level of being comfortable. I would not even need to talk to her. However, their mother has repeatedly said that she does not ever plan on meeting me. She said that there is no reason for the 'two worlds' to ever meet. She has told the kids this as well, which has made the kids feel that their father is 'a bad parent' for wanting to have me be with him at such functions. Except for these instances, the kids and I get along well. My question is: Do you agree that meeting their mom in such a way would be a good start to lowering their anxiety?

while it would be good coparenting for you to meet their mother, the fact that mom is making such a big deal about never meeting is creating anxiety for the kids, therefore any situation in which the two of you could meet would create anxiety for them because they would be put in the position of wanting to honor their mothers wishes of never wanting to meet you. it is best not to push it. welcome to psych central. you will find that we have several forums where you can post about your concerns and receive feedback from other members. you will get a lot of support here. again, welcome

Their mom should keep her apprehensions between her husband and herself and not involve the children. Children have the unique ability make everything their fault and her letting them know this is obviously making them uncomfortable.

In my opinion, it's best not to push because she'll voice her thoughts around the kids and worsen the situation. Discuss it with your boyfriend, but be careful about creating any bad feelings because it sounds like they'll just get passed on to the kids.