We sent out our STDs at Christmas and made a point of addressing them only to the person we were inviting (didn't write "and family" or "and guest" on any of them) to leave ourselves some flexibility with our guest list, but our intention was to invite significant others only when we knew them well and to only give +1s to the wedding party. Similarly with children, we wanted all the cousins there for sure (he has cousins down to age 3), but didn't necessarily want everyone to bring their kids. Now we're getting our invitations pulled together and it looks like our planning was perfect (numberswise), the party can have +1s, and that's about it.
I think we dug our own grave. Now our twenty-something friends (who, I guess, don't know better?) are emailing us "I got your save the date! My boyfriend and I are so excited to come!" .... your boyfriend isn't invited, we didn't even know you were dating someone. And my older cousins (I have cousins up to their late thirties) are wondering if they can plan for their kids to come along. I'm a bit more okay with the second cousins, but that opens a can of worms with family friends etc.
I've seen a lot of discussion about old or distant friends inviting themselves...but what do you when someone who is invited is trying to expand their party?