I uses the business version of Office 365 for e-mail. It works well. I never have a problem with e-mails not being delivered or going into a SPAM folder. I am not saying your family did anything wrong. What I am saying is e-mail works well for some people.
Yeah, unfortunately that seems to be the best way to handle this kind of thing but unfortunately that costs $6/person/month so our ~50 person casual email list for organizing fantasy football and family reunions would cost almost $4k/year.