EMG91215: What you are planning is not really all that unusual. There is standard etiquette for this situation.
First, I am assuming that by “family only” you mean parents and siblings, and maybe grandparents — maybe a dozen people in total. If someone who is invited to the reception ends up chatting with someone who attends the reception only, the latter person should think “but of course she would be there: she’s the bride’s sister!” rather than “why did she get invited when I didn’t?” A reception-only guest is more likely to think the latter, if every third person she talks to was at the wedding ceremony, than if a bare handful of fellow-guests were there.
Second, you should never invite anyone to only part of a social event. So you must treat the ceremony and the reception as two separate events. The easiest way to do this is to separate the two events by time and place. You do not want to have guests for Event B arriving during the wrap-up of Event A, or walking into an obviously pre-used party space. Since the ceremony will be presumably in the church nave, and the reception in the fellowship hall, space should not be a problem but you will have to manage the timing carefully. Schedule the reception long enough after the ceremony that you have time to get down into the hall to greet your guests without having to rush over, but not so long that your ceremony guests will have made obvious inroads into the canapes before your reception-only guests begin to arrive.
Do not send Save-the-date notices. These are usually in bad taste or bad judgement, but especially so for a family-only ceremony. Tell your family individually: it is much more personal, and you do not want to treat them like customers receiving bulk mail-out advertizing. For family that you may not see, write them a personal note telling them your plans.
If you are planning a rather formal reception, the invitation should read
(Host and) Hostess
request(s) the pleasure of the company of
—space to write in the names of the guest(s)
to a wedding reception for
at Thus-and-so Church Fellowship Hall
on Saturday the thirty-first of September
with little variations in wording depending on who the hostess actually is. The words “pleasure of the company of” are used instead of “honour of the presence of” precisely because this is a reception only, not a ceremony, which the words “to a wedding reception for” makes abundantly clear.
If the ceremony is informal, the invitation is properly worded as a personal note from the hostess:
Dear guest(s) name(s)
I am having a reception for Em Gnumbers and Future Intended on the afternooon following their private wedding, and would be delighted if you were able to come. It will be at Thus-and-so Church Fellowship Hall on Saturday 31 September. I do hope to see you there,
You will run into some internet-etiquette advice that you cannot use the word reception because you are not inviting people to the ceremony. You can safely ignore that advice: ladies have receptions all the time. While receptions do follow other events such as official ceremonies (not just weddings) and theatre opening nights, they also are held for their own sake. A “reception” occurs any time a hostess “receives” guests, and there’s nothing more important going on at the party to give it a more impressive name. But if you like, you can also call it a “tea” assuming that you will be serving tea and coffee as well as pickups.
I must say, you are clever to ask your questions first, instead of coming back when you discover you are locked into problems by things you have already done. Because it so often comes up in when people do ask later, I want to point out to you the write-in line on both kinds of invitation, where you actually write the names of the guests. If you choose instead to use the slightly-less-gramatical-and-less-formal wording that so many invitations use:
request the pleasure of your company at
then you need someplace to write the names of all the invited guests. The outside of the envelope does not work well, because the names of children and lovers do not properly belong on the outside of an envelope. So if you choose that wording, you must get the kind of invitations that come with two envelopes: you write the guests’ formal names on the inner, unsealed envelope; and just the name of the postal addressee on the outer envelope.