My only thought is the following:
Open up the phone, and with a cue tip clean the contacts - there are recommended ways to clean contacts of any types on the Internet, see what is suggested. Clean the Sim slot, clean the Sim contacts, and maybe there is something wrong with the Sim itself.
Out of curiousity, if you shift your sim card to one of your children's phones and see if it functions properly in their phones. If it does, it is probably something with your phone, and I would start with the contacts of the sim slot, or it may also be the phone itself.
If it doesn't work reliably in your children's phones, then it is most likely the SIM. Just thinking down this route because you say a competitor's sim works fine, so I begin to wonder if it is the Sim card itself.
Those are the only trouble shooting options that come to mind to me.
A repair shop that does repairs on cell phones would also likely have the tools to test connectivity, but you will pay a minimum bench charge to just start the testing.
Good luck and let us all know how it goes.
Full disclosure:
I am not a qualified tester of phones, just a user like you who has been through a similiar issues with Sim cards on phones.
Best of luck:
Bruce