It's changed who she is in their minds, and it clearly has an impact on her relationship with them

Had you not been straight with them, this would have been your outcome too. And just like cheating, lying or distorting the truth eventually gets found out. There's plenty that I'm sure who would get on here and indicate age as being the factor. Age plays a role for sure, but even if your children were 7 and 10, they deserve the truth albeit with less detail or more explaining depending on the child.

But there are very few people on this planet that you should strive to shoot straight with. Your children are part of that group. So is your spouse, which is why cheating hits so hard when it happens. So, you will do right to be straight with your children about the situation.

They stay in touch with her and do things with her, but it's clearly out of obligation (at least it's clear to me)

Remember that she's the parent, she's going to need to be the one who repairs the relationship. There's no point in asking your children to be more adult than your former wife. Your children may be doing out of an obligation to maintain some semblance of normalcy, may be doing it out of respect for you and not knowing other means to show that. But your children are going to have the relationship with your former wife, that your former wife forms with them going forward. Relationship inertia is a thing and your former wife would be wise to use that to help repair the broken trust and the attempt to be deceitful with them. That inertia eventually will run out of steam and if your former wife spends too long fuming over the revelation, she'll lose any grace she's been given to help in the repair. Remember, your kids are smart enough to understand that mom wanted to "hide" this from them. That's in their heads be it they say it or not.

I feel bad for her, I really do.

Then you would do well to remind her that she's got to take control of this situation and earnestly repair this relationship with her children. If you do care still for her in some fashion, then reminding her she's got repair the trust she has torched with her children and not attempt to hide from it. I don't know your wife, but ultimately, whatever relationship she has with her children is exactly the one SHE CREATED.

I believe the kids have a right to know why their lives were suddenly and completely changed out of the blue

If you value your relationship with your children, you would do well to not lie or betray their trust. Especially now. It's easy for them to become really jaded from this experience and see faults in all of their parents. It's a popular idea that there's the good parent and the bad parent, but there is parent A, parent B, and each child. You are all your own separate beings. Again relationship inertia has them "flock" to you at the time, but as this whole thing ages, it'll start to take a personality of its own and affect how they see paternal relationships in general.

It's good that you have empathy for your former wife and perhaps if you wish to help the relationship between your kids and their mother, you can share your empathy that you have as a guidance for your children. Best of luck.