Hi! I did a little research on this subject & found this product and articles:
https://allnoisecontrol.com/animal-shelters/
https://www.controlnoise.com/2011/08/22/soundproofing-an-animal-shelter/
https://acousticalsolutions.com/soundproofing-a-dog-kennel/
https://www.aspcapro.org/resource/shelter-health-animal-care/three-things-consider-about-your-shelters-soundscape
I don't know if any of these Andsuggestions would work or the cost, or even if it could/would be approved by the inspectors in your area, but they may be worth a look?
I did have another suggestion... Making the assumption that you are non-profit you probably have a board. On that board you may (an probably do) have a facilities manager or contractor type person. Tap him/her for some suggestions... Also, look at the students in your area for some suggestions (we have a few colleges in our area). Also, it could be that re-arranging your current facility would benefit the cats & the dogs? For example, you may need an indoor location for dogs (birthing, puppies, sick?) that can be converted or swapped for the cats (off-season) & then only needs sound proofing on 2 sides or 1?
As for making your 'case' for the change, other than reducing the stress on the cats & dogs... Check into illnesses that can be passed from dogs to cats (and vise-versa), stress illnesses, added adoptions, lowering medical needs (stress cost reduction) for stressed out animals & illnesses that are made worse by stress, etc.
Sometimes a change like that cannot be quantified, but can be 'understood' by those who want the best for the animals! Good luck!
#OrganizationalManagement