Hey Dianne157,
Thanks for using Apple Support Communities! I understand you're running into a couple of issues using Mail. I certainly understand how important it is to be able to send emails out without issue, and I'm happy to help.
To start, when sending a group message is it always the same contact that doesn't appear? If so, are you able to send an email to just that contact? If not, double check their email address is correct.
I also recommend double checking that Mail is your default email as well. You can see how to do that here: Change the default browser or email client on your Mac
Also from Mail Preferences > Composing double check that "When sending to a group, show all member addresses" is selected.
Thanks again, and have a great day!