Vegetarians, esp. vegans, often find themselves conflicted when faced with feeding dogs; even more so when feeding cats.
The long-term health of cats
depends on them receiving meat. They are obligate carnivores, which means they
must consume meat for their health and survival. Their dentition is that of a carnivore: tear, shred, swallow. Although I've had a few cats who would eat, as add-ons, cooked corn or raw cantaloupe, they were much happier with chicken, cottage cheese, hard-boiled or otherwise cooked eggs, or regular cheese. (Or, of course, commercial cat food....)
The long-term health of dogs is harder to predict; dogs are, evolutionarily speaking, scavengers. They have the dentition of both carnivores and herbivores, like people do, and their stomach acids can break down even questionable meat (their stomach acids, according to a phone call I had with a U. of Penn. researcher several years ago, are anywhere from 2x to 4x as strong as those of humans).
However, many vegans and other vegetarians have found that their dogs enjoy more robust health and resistance to disease when fed meat (usually raw meat), vegetables, fruit, etc., in a specialized diet tailored to the individual dog, or at least breed/size/activity level of dog. This statement is based on several years' worth (since 1998) of articles in
The Whole Dog Journal ("A monthly guide to natural dog care and training"), a newsletter on dog health, positive training, management, research, food recommendations--All Things Dog. https://www.whole-dog-journal.com/
Please, for the health of your cats, give them meat.
Regarding the dogs, if they appear healthy on the food you're giving them (complementing grains/legumes for complete protein?), it's probably fine. Maybe a few eggs throughout the week just to make sure about the protein quality (I base this statement on both Frances Moore Lappé's
Diet for a Small Planet and Laurel Robertson's
Laurel's Kitchen; The New Laurel's Kitchen).
I haven't researched vegetarian diets for dogs, b/c Berners do so much better with meat. I purchase (when I can...$$$) ground-up byproducts from grass-fed beef from an individual ranch. These are "innards" that the ranch has found don't sell well as people food but sell very well as dog food. Vesta won't touch this $$$ pet food; she prefers the Merrick canned food (sourced and made in the U.S.). But Vergil is a grass-fed beef guy. Whenever the ground-up innards appear in his bowl, he is visibly delighted.
Personally, I eat very little meat. Part of a chicken each week, I think, except when DH decides to cook dinner and I find a piece of dead steer on my plate. I take a few bites--he did, after all, make dinner--but give a few tidbits to the dogs and the cats and tell him that I'm full when there's half a piece still left. He's happy to "help out." Bleah. (Just to let you know where I am on the carnivore => omnivore => herbivore spectrum.)
Good luck with the injured sheep / collie / Lab dynamic.
Cynthia