I think it's unfair to keep a dog inside 24/7 personally. Unless, like Prince, who had a MAJOR medical condition.
Dogs will be DOGS! I don't care if they are 3lbs or 100lbs... they need fresh air too. Imagine keeping yourself indoors for your entire life. You wouldn't do it to your kid or yourself, why do it to your dog? Humans have allergies too, and we still will go outside. I suffer at certain times of year, but I take medicine. I could never be cooped up inside all the time, and Jackson couldn't either. There's a little 4lb Yorkie that goes to the dog park every day and has bad allergies but he LOVES his visits to the park every day... so the owner just has to go home and clean him off when they get home. No biggie.
Just because our dogs are small, they are still dogs, sharing 99.8 percent of the same DNA as their wolf ancestors. And sometimes I do think people forget that fact. Yes, I treat Jackson like my baby and consider him like a kid to me, I spoil him with treats, toys, and everything else above, but first and foremost, he always gets to be a dog first. He wants to get muddy? I let him. He wants to go swimming? I let him. I've never held him back from anything unless it was truly going to harm him of course. I would never let him just run loose or anything and eat everything he wants. But that's where a great "leave it" or "drop it" command comes in.
Basically just because your dog is eating a bunch of stuff outside doesn't mean you should keep them from outside. You could train her, or keep her mind occupied with other things outside. Jackson always seems to find things outside too but I offer him something better like chicken or a treat to drop whatever he has. If it's something like a stick, I just let him chew on it. Certain bugs I encourage him to eat, LOL. If there's one in my room, he usually will take care of it for me
They were bred to hunt and kill rodents. Or I keep him on a 50' leash - just use preventative measures. Make a small fenced in area, etc.