For water bottles, if you take one bottle, dump out the old water, pour in the new water, put the filled bottle into place, and go on to the next one: that takes a long time.
Water dishes are much faster to dump and refill. For some animals, switching to dishes makes it much faster. (Example: rabbits can drink from a bottle or a dish. Rabbits tend to spill small water dishes, but dishes more than a certain amount big can be heavy enough they do not get spilled.)
Animals that drink from a water bottle can often drink from an automatic watering system as well. For example, with rabbits, you can fill one bucket that sits above several cages, and the water flows down through a tube to each cage, where the rabbit can drink through a special valve. Topping up the bucket would be much faster than dumping and refilling several individual water bottles.
If you need water bottles rather than any other water source, you may be able to save a little bit of time by doing them in batches. Unscrew the lid of one and sit it upside down to drain itself, then open the next one and put it upside down... Once the first one is empty, you can go along filling them up again and putting them back on the cages.
If you have to carry water bottles somewhere to dump out the old water, consider dumping them into a bucket and carrying the whole bucket somewhere at the end.
If you have to carry water to fill the bottles, consider having two bottles per cage. You could fill bottles at the faucet or hose, then go switch them out, then sit all the old ones upside down/open to drain themselves. This can be faster than running water into a jug or bucket, then pouring it into the bottles. If you were carrying each bottle from the cage to the faucet and back to the cage, having two bottles per cage will save time there too.
Freezing weather changes things. Automatic systems need heat, bottles and dishes freeze and need to be thawed. For cold weather, the best time-saver I know is two dishes or two bottles per cage or pen. Bring out fresh ones, take the frozen ones into a heated place and let them thaw.
cooking for and feeding the dogs,
Can you cook enough for several meals at once, then refrigerate the other portions to feed on the next few days? Or do large batches at once and freeze them for later?
watching them eat so they don't fight
Feeding them in separate places can let you skip this bit. You could use individual crates, or shut them into separate rooms, or let one eat indoors while another eats outdoors, or tie each one to something (stair rail, doorknob, different sections of a fence).
Depending on how fast they eat, you could let one eat in the kitchen with the other(s) shut out, then change which one is in, and you do the dishes or cook your meal while they are eating (that means you are there to switch which one is getting to eat, but you don't need to actually watch them if the others are shut out.)
For some dogs, training can also solve the problem. It takes longer while it is happening, but eventually can make things easier. For example, feed each dog on a mat, and train them that they must stay on their own mat until you release them. I would probably do something else for now, and consider training when you have more time at a different season (for example, after the baby goats are weaned, so you don't have to do their bottles anymore.)
bottle feeding baby goats
If you don't already have a rack to hold the bottles, you might consider one.
I am not going to suggest that you cut down on breaks.
But do maybe consider whether you can time your breaks to save a bit of time. For example, if you give food to dogs, or bottles to baby goats, they may be able to eat while you are taking your break, and then you can go pick up the dishes and un-separate the dogs, or collect the bottles from the goat babies. It's the same logic as starting the laundry and the dishwasher, then taking a break while the machines are working, then being able to start another load after your break.
For any of the chores, sometimes it is worth thinking about how you can save time by doing them in a certain order (like if you can clean a stall faster while the animals are eating, because otherwise they try to "help" and slow you down.)
What are methods or machines you've used to cut down on barn chores time?
If you have to carry things back and forth, think about ways to take fewer trips.
For example:
If you carry jugs or buckets of water, can you run a hose instead? Or use a cart with wheels to carry more water at one time?
Try to store things close to where you need them (like chicken feed next to the chicken pen, or pitchfork and wheelbarrow next to either the area to be cleaned or the place you dump it.)
Remember to take what you need when you go (example: bring the egg basket when you are going to the chicken coop, rather than having to walk back for it later.) Sometimes it helps to carrying a pencil and paper to make notes, or use a cell phone for that purpose. A note like "chickens need more grit soon" can remind you to bring the grit the next time you walk that way, instead of making a special trip for it.
veterinary care for injuries if needed
If this happens very often, you may want to change things so there are less injuries. What you can do will depend on the kind of injuries-- fixing a sharp nail is always a good idea, but it won't change anything about animals that cause injuries by fighting.
For any injury that happens, you might consider how much care it will require, before you decide about treating it at all. There are times that dispatching the animal is the best choice (reduces suffering for the animal, reduces work for you.) There are other times when treating the injury is the obvious choice (small treatment, animal gets back to full health quite quickly, this saves you having to buy or raise a replacement animal.) And of course there are cases where the "best" choice is not obvious. You might also need to consider how busy you are at the time.
