There are situations in which some priests will counsel some people to go to the wedding for the sake of preserving the relationship. The argument is that if the relationship is at least intact, you have a better chance of being able to influence them in the longer term, than if the relationship is completely severed. Other than that situation, one should not attend an invalid wedding, and I believe in ALL situations, one is not permitted to participate as an official witness to the wedding (which means you can’t be in the wedding party, even if you do attend). Whether your situation is the type where not going will result in the obliteration of the relationship, and whether it is necessary in to compromise and attend this particular wedding, we couldn’t tell you. That is where the trusted priest might be of some help to you. The other factor is if you have children. It is one thing to attend an invalid wedding as an adult, knowing that what is happening is not right. It is quite another to bring a child to something that causes them to be confused about right and wrong. Again, that’s not to say it is completely black and white. But there is a heavy weight towards not attending.
Personally, I wouldn’t touch it with a 10 foot pole, and I’d be very straightforward with my mil about it (actually as the son in law, you would probably be best to have your wife do the explaining, and you be her support). I definitely wouldn’t let my kids witness the wedding. Of course, I know that many people are not as straightfoward with their families about their faith as we are. I am a firm believer in letting people know the real me. So it does not come as a shock to anyone when I make unusual decisions based on my faith. One side of the family is very big on integrity, and understands that following your conscience is a matter of integrity. The other side of the family is getting used to us being really different in how we think, and they are starting to understand that we are capable of loving them despite our differences, and they are capable of loving us, even though they think we’re crazy. And we have declined 2 weddings, and we have gotten past it.