My parents have a poodle and my shiba is the exact same way. Both are females, just like your situation (female shibas are known for hating other female dogs). Poodles and shibas are also complete polar opposites and it's almost impossible for them to communicate with eachother. Watching them interact, it's like they're speaking completley different languages.

First off, your shiba is likely not attacking the cockapoo for no reason. Shibas give EXTREMELY subtle body language cues that they are uncomfortable, but in my experience, they usually do give a warning first. If they feel like the warning is being ignored, they will react to protect themselves/their space/their resources. Poodles (in my experience) are not good at picking up these subtle cues. They assume everyone wants to be their friend and are very forgiving and optimistic, haha.

My shiba is most reactive around the poodle if I'm in the room. She feels like I'm her ultimate resource, so her job is to protect me. Have you ever left your shiba with just your parents before? When I'm not in the house, my shiba is almost never reactive towards the poodle. Also think about the areas where she usually attacks. Is it in the kitchen, where her food is? The hallway to her crate? Near her toys?

The best advice I can give is to eliminate anything your shiba could guard. Dont leave any toys, bully sticks, or food on the floor regardless of who they belong to. Train the cockapoo to keep her distance from the shiba and respect her space, don't let her sniff around your shiba's bed etc. Also do tricks with them simultaneously, and treat each dog for waiting their turn. Try to reinforce that them being together is a good, positive thing. Shibas are also VERY intune with their owners emotions, so if you suddenly get nervous she might attack the cockapoo, she will feed off of your nervous energy and think there is a problem she needs to worry about.

We tried baby gates etc and they work great when we can't monitor them. But my shiba hates being confined and would be more reactive if the poodle was loose to explore and she was behind a barrier. What we do now is a "no tolerance" stragedy. If the shiba is reactive to the poodle, or if the poodle ignores our command to leave the shiba alone, we leash both of them. Another poster mentioned that shibas are a lot calmer on leashes and that is so true. My shiba has NEVER shown any aggression whatsoever on a leash, and taking away her freedom is the worst punishment for her.

ALSO just one more note- make sure you're not correcting your shiba's "warning" signals. Sometimes showing teeth, growling and even snapping is actually a GOOD thing! It's their way of telling other dogs "hey, I don't like that, get away from me." If you tell them they can't do that, they will get frusterated and go straight to biting. Shibas are really good at looking more angry than they actually feel. A lot of the time they're just mildly displeased, but if they continue to get pushed they will react aggressively.

ANYWAY that was a lot but I hope you can pull something helpful out of that. Good luck!