I would find it very odd to see kids at a shower. Around here, they're specifically adult events.
That said, I don't know why your choices would be "lots or none." Just like a wedding, or a barbecue, or whatever, inviting two kids you're close to doesn't mean you "have to" invite 15.
That's a tricky one. I say leave it to the parents to keep their kids behaved/entertained if they MUST bring them. You could consider providing coloring books/crayons or bubbles, something cheap like that. Ultimately, the party isn't for the kids, it's for you.