Hey there RonEdwards,
Thanks for reaching out in Apple Support Communities. I understand you’re having some unexpected Handoff issues. I’ll be happy to help.
Sign out of the iTunes Store and iCloud on both your Mac’s and restart. Sign back in and see if this has any impact on the issue. To sign out of iTunes, go to iTunes > Account > Sign Out from the Mac menu bar. To sign out of iCloud, go to System Preferences > iCloud and Sign Out.
If the issue continues after that, you’ll want to reach out to Apple Support using the following link to continue to look into this with you:
Contact Apple Support
Best wishes.