I think you can explain the church seating without offending. It seems that you need your mother there, and with her and your daughter, and you and your husband, perhaps the only other person to include would be her godmother. Simply tell everyone that only 5 people are allowed, including the child who's being confirmed and her sponsor. It sounds like it's a very small building, and that is beyond your control.
Then, you can either just have cake and punch at your house afterwards, or you can invite everyone to a "bring-your-own-picnic" at your place. Just tell everyone that since there are so many food preferences, allergies, etc that you've decided that everyone can come and bring a picnic lunch for their own family. You can decide if you want to specify a cold lunch (sandwiches, vegetable salads, pasta salads, wraps, cut up vegetables) or if you will have any grills going for hot dogs and hamburgers if people choose to bring those. But if you won't be providing a grill, make sure that you tell everyone to bring food that won't require cooking. You can just get some big coolers or washtubs or barrels or wheelbarrows and fill them with ice and sodas. That's pretty inexpensive. If you can, provide paper plates and napkins.
I think that would be extremely reasonable. Make sure to take photos at the ceremony (or before and after, whatever is appropriate and respectful) and have them available for viewing (on a laptop for example) at the party. That way your daughter can celebrate this important event with her relatives, receive gifts, and all you've done is welcome people and buy some ice and soda and set out blankets and chairs. I would not be offended to a bring-your-own-picnic but I would want to understand that there wouldn't be grilling, or that there would be, and that if my husband wanted a beer, only sodas would be provided and we were either welcome to bring our own beer or else we'd be told this was an alcohol-free child-friendly party. As long as the rules, so to speak, were clear, I'd be happy to bring the food for our own family. You can even mention that if people have lawn chairs or blankets, bring those too. Try to decorate a little; the dollar stores have banners and pretty paper plates and pinwheels and things like that. Be festive but frugal for your daughter.
Make the invitations for the bring-your-own-picnic only, be specific but positive (don't say "money is tight", just say "we're hosting a bring-your-own-picnic party and you're invited to help celebrate ________'s confirmation at our house from 2 - 7 pm [or 5 - 8 or whatever]. Bring enough cold ready-to-eat food for your family, such as sandwiches, wraps, salads, vegetables, and we'll provide sodas and ice and plenty of blankets for seating. If you have lawn chairs, feel free to bring those. We won't be grilling as there will be too many people and too-limited grill space, so cold prepared food only please, just enough for your own family." You don't even need to worry about RSVPs this way.