Working for a Dr

You shouldn’t be inviting anyone to just the after dinner portion. If you can’t or don’t want to invite them to the whole thing, I wouldn’t invite them to any part of it.

You don't have to invite the two physicians if you don't want to

That's up to you. Are you close with them? Do you have room in your budget?

Also, anyone invited to the wedding should be invited to the full reception, not just the part after dinner. It gives off a vibe that they're just not as important as your other guests.

Will your ceremony only be close family and friends? Reception only guests' feelings could be hurt if that's not the case

You can do whatever you want. I think it's odd to invite people to only the reception and not to dinner or the wedding. However, if that's what's normal for your region/circle, go for it. I just think it would be difficult to manage who comes to the ceremony, who comes to the dinner and who comes for dancing. It sounds like you'd have 2 or more guest lists. What if your reception guests show up early and have to wait for people to finish dinner. That would be awkward.

I’ve been to quite a few weddings where close friends and family are invited to the ceremony and dinner and then friends are invited to the reception after dinner portion to help celebrate. It’s pretty normal where I’m at.

No one should be invited after dinner. That’s super rude and gift grabby.

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Agreed. This feels weird to me. I would be pretty insulted if I was invited to a wedding but wasn't allowed to come to the ceremony or even eat dinner?