You need to raise the FP with your new pet before they will herd more than one animal. Another easy way to do this besides feeding them and picking them up everyday is to buy the toy that will become available at Raul's or Diego's store. The cat will have a bell, and the dog (both types) will have a bone. Play fetch with them to raise their FP.
I always played with them at night after I was done with my chores, and you can do it as many times as you want to, it just keeps raising their FP.
A cat will herd 5 chickens or chicks when it has 10 hearts (I think it will herd one at 500 points, I know mine didn't show a heart when it started taking a chicken outside), a small dog will herd five sheep or alpacas at 10 hearts, and the big dog will take care of 5 cows.
The pet playpen is great, I put my second dog in the playpen after the animals are outside and its heart level is rising faster than playing with it. With three dogs, the correct dog doesn't always catch the bone and the other two are at 10 hearts already. To bad you can't play with the dog and bone in the area. It just isn't interested.
My animals would never leave the barn if it wasn't for pets. There's no way I'll waste all day pushing animals in and out - in my SI, nobody ever went outside at all. But full pets is way too many for Konohana so they're in my way. But I can't stop feeding them to make their hearts go down and stop standing on my feet while I'm trying to milk a cow. Oh well (*toss a dog over the fence*).
I didn't like pushing my animals in and out at first, like you Murasaki, I never let my animals out when I played SI at all. But in this game it doesn't take that long since they have a set pasture already that they have to stay in. I only ever get one large dog, one small dog, and one cat. I just train them up so that they'll herd all my animals everyday.
I don't think that's enough if you have a full Bluebell farm with 16 animals and 10 chickens. But yeah, the animals are easy to level up - even if you don't put them outside (and their food is cheap). I've never had any animal get sick or depressed so dunno if they'll do that if kept barn-bound.
In Grand Bazaar they ate like pigs inside so I mistakenly thought they would eat outside but they ate just as much inside. I had three dogs and two cats and everyone went outside.
If you have 16 animals in Bluebell, I think you need more than one of each pet. I had a big dog at 10 hearts, and a cat with 9 hearts for 4 years in Konohana. I got two sheep in year five and realized that, even with treats, their hearts were rising slower than the new cows and chickens that were outside everyday. That was when I got my small dog.
I want my alpacas to have 10 hearts as soon as possible for cash flow realons so I got the second small dog. It brings out the sixth animal and then I pt it in the playpen. Everyone is getting hearts quickly (pet and livestock).
I'm never home until after 4 a.m. anyway so the large group of pets is no problem for me. You'd have to ask Kana what it's like until I get home but he never complains.
I miss the Harvest Sprites! Though they weren't totally reliable (always did my own watering of my plants cuz they'd leave some spots dry). k fine, they were actually a pain.
All my pets are max hearts by just feeding them so they all do their work. I'd throw them in the Bluebell playpen to get them out of my way but that took a while plus they'd escape! Wish I can sell them back.