I think it's a shame that you even have to tell people that a shower is not for children! But I think you have to hold firm - it's not just that it's an expense, it's that it's inappropriate. Nursing moms should of course bring their infants if they need to, but that's the limit.
Are you using purchase invitations or are you creating your own? You can do a lot of things easily through a print-on-demand service or your local quick printer. If you say something like "Join us for an elegant ladies luncheon at Chez Maurice in honor of Stephanie's upcoming nuptials" and perhaps print the menu (the absence of chicken fingers and fries ought to convey the overall atmosphere), that's a start. Make sure the invitation is just addressed to the recipient. If it's just women, it should be easier to manage - couples' showers start to look like family affairs.
You could put (and it's a shame if you have to) "Sorry that the function room cannot accommodate children") but you can also hope that you get accurate RSVPs so you can set up the room. If someone says she's coming with her 2 kids, then you can address it with a pause, then a surprised tone, by saying, "Oh, my…well….We never imagined this to be a children's event. It's really for ladies only and we can't accommodate children either with the menu or the physical set-up. I'm sure you understand that's why the invitation was to you alone." If someone pushes back, you have to be firm and say, "I'm sorry that we cannot include children. We hope you can get a babysitter so that you will be able to join us to celebrate with Stephanie." If 4 of you are hosting, then 4 of you can divvy up the responses as needed.
But you must agree on verbiage to use. No one can cave in if you have turned others down.
Yes, of course gifts should be opened at the shower. You can start during the luncheon if necessary if the bride gets through enough of her lunch to make it possible for her to start. Then she continues while the restaurant clears, serves dessert and pour coffee.
One theme I've seen several times is an "Around the Clock" shower - each guest is assigned a time of day or night (9 AM, noon, 5 PM, midnight, etc. - just create as many times as you have guests). The theme creates a sort of a game, but allows guests to choose very freely among the many gift choices. So people who get 11 PM or 1 AM can choose lingerie if they want (or luxury bath items, towels or anything else). You can make sure prudish or sensitive Aunt Shirley doesn't get one of those times if that's a concern. Others will wind up choosing a coffee maker or wine glasses or salt & pepper shakers or a picnic basket or whatever else is on the bride's registry or just something they want to give. It's not restrictive, because a coffee maker could easily be for 7 AM or 9 AM or 7 PM. It's really okay to pre-select some times for people if you know that someone has a gift in mind. The rest of the guests don't have to know! Then you keep a master list and just call off the times to have the bride open gifts in order, or you include a sticker or a hang tag that can be tied on the outside of the gift so that the time of day is obvious when the bridge chooses gifts randomly.
This provides a theme without you having to create special decorations. Yes, you can have a drawing for the centerpieces - give out a ticket or just draw names out of a hat. If you are giving out party favors (which you do not need to do), I've seen people put a sticker or tape a penny to the favor or even under the chair.
There's the standard "shower game" of collecting all the bows and ribbons to stick on, and through, a paper plate which is then used as the bouquet at the wedding rehearsal - something for the bride to carry and hand off to the maid of honor. It's not new, but a lot of people like it and consider it traditional. Assign someone at the shower to do this (provide paper plate, scissors, tape), and also assign someone with a pad and pen to record all the gifts and who they are from. Don't rely on cards not getting separated. Also have a special place for just gift cards - these things have a way of disappearing either because of dishonest wait staff (more common at weddings) or because they are so small. This is a huge service to the bride and something that's easy to delegate to someone other than the 4 of you hosting it.