Maybe a complete opposite approach is worth to try. Focus on what you want. I assume the interaction between Relative and your children is as safe as they are with you. (Keep in mind that things you want consist of positive acts that create synergy, altruism is key).
What could create a stronger bond between Relative and your children? What do you like Relative for yourself? What does Relative bring for positive things in the world with his/her existence? Focus on that, keep that in mind, tell that to your children. What can you do to make both Relative and your children experience the best of what the relation of Relative <-> children can be? Use your will power to create just that. How would that feel, to you, to Relative, to your children?
I believe that if you do all this with a sane (knowledgeable) mind, you will make the most out of the situation.
Relative is thinking about a pink elephant in the living room, which isn't there, but the idea is bothering her. Now you are talking about a pink elephant in the room, which isn't there, but you are now also thinking about that pink elephant int he living room. Relative behaves different because of the idea of the pink elephant in the living room, which is very stuck in her mind. You want to explain her behavior to your children by discussing the pink elephant sympathetically. Now there are 4 of you, thinking about this pink elephant, which ins't there. Relative wants to hold on to the pink elephant, because she is afraid to let it go. It is affecting you, and you are affecting your children, so the elephant is to stay. Now your children have to think about the pink elephant as well, which isn't there, but it helps them to understand Relative's behavior...
Logically reasoning you should loose the pink elephant and the problem is solved. Stay as close to the solution as possible. I understand this isn't easy, and it is not Relative's choice to have that pink elephant in the room. But she wants it to go away as well, but she is afraid to think about letting the pink elephant go. If you want a practical answer: Tell relative to calm down when your child sneezes. No discussing of the pink elephant required. And you are the example figure to your children. You define what is normal behavior (at least your children trust you more in it, than they do trust Relative on that matter).
Yes, Relative will be annoyed by the fact that you don't believe in the pink elephant. Because she thinks that pink elephant is required to protect her from illness (or whatever her fear might be).
why is Mommy ignoring Relative? what's up with this pink elephant anyway?
There is a nuanced difference about ignoring and not going along with it. You can show sympathy for the fact that Relative suffers from a pink elephant in the living room. That doesn't mean you agree it is there, you agree with it being a burden to Relative. So you stil show empathy, but you stay with the solution of removing the pink elephant.
still sends no clear message to the kids
Yes there might be conflicts. But is this about avoiding conflicts or about doing what is best for your children? Do you want your children to learn how to get rid of pink elephants that jump around in their own minds? To track them down, face them and remove them by focusing on what they do want. Or do you want to learn them that other people should mind those pink elephants inside your childrens mind, or otherwise your children have all the right to become annoyed towards those people?
Now to put this more clearly I am convinced that everybody has pink elephants in their minds. Because everybody has fears (or atleast 99.99% of the population does). Relative has big pink elephant and yours, your childrens and mine may be quiet a bit smaller.
I think by acting solely towards Relative about what is the normal behavior (on a moment is matters) is a clear message for your children when they witness the situation. They will also feel that you have a strong mind and will. You will be their example, they can trust you. You know what is right, and you dare to act upon it. You don't burden your children with all the problems in the world, but you teach them to focus (and therefore experience) all the great things life has to offer. So they will dare to do the same. meanwhile you have shown your empathy as well, which your children will also show towards others that act upon their pink elephants.