How to separate meat from vegetables in a soup? I love to make a nice chicken soup.

I take some chicken legs, carrots, leak and celery, a few herbs and of course salt and pepper, and I just let it boil for like 4 hours.
I then sift the soup to take out all the vegetables, skin, bones and meat. This way I get somewhat of a clear soup.
Then I take the chicken and put in all the chicken meat back in to the soup.
The thing is, I often have a hard time separating the chicken and vegetable "mash".

My question: is there an easier way to do this? I was thinking about putting the chicken in some kind of net, but couldn't find cooking nets online.

Are they maybe called different?

Is it an option to do half/half? Boil the chicken in 1 pan and the vegetables in a second one?
Since the intermingling of the flavors is what your soup is about, and you want to remove only some of the solids (the chicken), a metal insert or colander might be too cumbersome. 

Boil bags are what I’d suggest - cheap, disposable, and will allow everything to simmer together nicely. 

https://www.amazon.com/dp/B071RJTTXH/ref=cm_sw_r_cp_api_i_8SdHCbFWV2C0R