How to Process Calendar Responses?

Hi, if I create a calendar event in my LOCAL calendar, invite someone, they “accept”, I never get the “acceptance”? Is there a trick to this?

If I create the event within my apple calendar, it’s hit and miss, sometimes it shows up sometimes it doesn’t.

I was hoping reverting to use the cal in “local folders” would sort this out? I’m willing to give up apple calendar to get invites / acceptances working better.

Any suggestions on what I might be doing wrong?

Thanks