Hi Tom, welcome to planDisney!
You are asking the right questions now to ensure that your family has a very merry Christmas vacation at Walt Disney World Resort. For seamless planning, all members of your traveling party need to be correctly connected as Family & Friends in My Disney Experience. I'm going to answer some questions and draw some conclusions intended to set your family up for success.
I understand you have a My Disney Experience account that currently manages your two children's profiles. It also sounds like your wife recently created a My Disney Experience account and made steps to connect with your children. There are two ways in which your wife could have added your children to her Family & Friends list. Because she sees "Invitation pending" next to their names on her Family & Friends list, it appears she clicked "Add a Guest" and "Find through my connected Guests." Because you are the person that manages your children's account profiles, you should have received an email invitation to connect for each child. Search your email account for emails from Disney Destinations with the subject, "You've been invited to connect with Family & Friends through My Disney Experience." If you don't see them, ask your wife to click "Resend" next to "Invitation Pending" in her account. Once you click the green "Accept" button in the email invitation, your wife will receive a "Your Walt Disney World Family & Friends Invite Was Accepted" email and she will be officially connected with your children as Family & Friends.
Only one person can officially manage a child's My Disney Experience account profile, but anyone connected to that child via Family & Friends can view and make plans for them (book dining reservations, purchase Disney Genie+ service, view Disney PhotoPass images, etc.) There's a short list of things only the managing account holder can do, which includes managing their MagicBands, downloading their Disney MagicMobile passes, and changing their profile image. If any of these things are a big deal for your family, Cast Member assistance is required to change the manager of a Disney account profile.
There's one more thing I have to mention, Tom. You mentioned that the grandparents were involved in setting up My Disney Experience accounts. Duplicate My Disney Experience account profiles are a common problem that can cause hiccups on Walt Disney World Resort vacations. If the grandparents happened to create a My Disney Experience account profile for your wife before she created her own account, those two presences need to be merged. If that's the case, please reach out to me directly for next steps. Helpful Cast Members at the My Disney Experience, MagicBand, and MagicBand+ number are also great at untangling My Disney Experience webs. Be sure to provide email addresses for all My Disney Experience accounts involved in the situation.
Plan magic; planDisney.
Jennifer