1. Kerry applied for an annulment after remarrying but it was either denied or didn't even reach the stage where it would be denied.
2. Having 2 kids isn't necessarily a deciding factor. It's not about the kids, it's about whether the marriage was sacramental.
3. The "granting annulments to rich people" thing is likely a myth. It's fairly easy for ANYONE to get an annulment, rich or poor, although that's a scandal in itself. The guidelines are interpreted to be very flexible.
It would be interesting to learn the final result. Did he just let it drop? Did the church deny it had validity?