"Just to be sure find out if the kids had to sign at the closing"

On the Sale. The kids obviously filled in W9 (or Mom did it for them) but that isn't the Sale Closing.

It certainly helps Mom if it turns out they used the 1099-S only as "distribution names" as a replacement for her doing the Banking. Then, she will still be able to use her exemption.

She still has a gift issue, though, unless you can allocate it well enough to avoid that part.