Hi there,
As a Owner of cocker spaniels my whole life (and i have worked with cockerpoos from time to time), i think its fair to say he prob gets it from the cocker side! they are notorious for being noisy, especially if they are unsure or nervous over something.
I always found the best way to deal with this kind of behavior, where they get fixated on something, weather it be barking, nervous behavior or any other situation where their attention is not on you but on the thing they are reacting to, is to bring the attention back to you. Avoiding the problem just means its still there and if you happen to encounter it again (as we cant control the world all the time) the behavior wont change.
With barking i normally, slowly, and very very gradually, expose them to the situation, no more than a minute or two at a time, but ~the entire time~ i am feeding them treats, talking to them, getting them to do tricks, anything to get their focus on me and not on the thing making them bark. My goal is basically to make me far more interesting than what they are barking at. Over time you can increase the time you expose them to the situation, always keeping them focused on you, until it looses significance in their mind as you are far more interesting.
I also, as a priority, teach any pup "eyes on me", with a verbal command and hand gesture (i use two fingers to point to my eyes to make and keep eye contact with the dogs) asap. so any time they start to kick off, i can instantly bring their focus back to me, and calm them down.
Get other family members involved, its something you can all do together! as a example, before you bring in the shopping, have someone inside and in place with the dog and treats on hand, to start the distraction the moment you come in, just a example :)
This also helps with bonding a great deal so its win win all round! It takes time and patience, but in the long run its tackling the problem rather than letting it stew
hope this helps!