My friend did this for her DD's 16th.
She met them at the door, and took their bags "for safekeeping", and left them in the hall, which has a lockable door from both inside and outside the house.
When the first guest asked her for their bag, she took her into the hall, and got the bag, the asked if she minded opening it. Of course, there was a large bottle of spirits in the bag. She joked "oh, you shouldn't have!" but then let the guest take the bag, but not the drink, which she said she would give back after the party.
She didn't have many asking for their bags, after that!
She did serve alcopops and beer at the party, alongside soft drinks. I think she catered for about 2 alcoholic drinks each.
I guess yours is different, because many of the guests will be over 18. But I don't see why you shouldn't ask to either check, or "check in" bags at the door. If they have brought spirits, just tell them they won't need it, as there is plenty provided, and you will give it back, when they go.