I just read the whole thread and have some thoughts. Sorry it is long, but I put in details and the reasoning behind the suggestions.
Dogs - what do you feed them? I have a medium-size arctic breed and I feed her grain-free - not expensive, Costco has two versions and my grocery store has a house brand. I mix them all together, she loves it and she is healthy. Dogs can digest plant material, yes, they are not obligate carnivores like cats are, but they do not digest grass seed. I trust your cat is getting a food meant for cats? They have higher protein requirements than dogs do. Dogs love cat food, as I am sure you have noticed, but they do not need the higher quality protein, so don't let them snack.
Walking - fall is a wonderful time to walk. You could combine dog and kid walks by walking your son to daycare with one dog, and walking to pick him up with the other one. That way both dogs get a 2 mile walk and you and your son have quality time together. You can freshen up in the morning when you drop the dog off at home, and drive, if you still think the drive is worth it after getting used to walking.
Car and gas - I started driving in 1967 - back when cars were mechanical, not electronic. A wonderful way to see what you are doing re the car and gas is keep a car journal - get a little notebook and keep it in the glove compartment. Have headings - I have Date, mileage (odometer reading), price, litres (gallons for you), cost and location. With this you can calculate all sorts of things - how much gas you are using, how much you are spending, miles/gallon (do it after a week of short trips and after a long trip, you will see a big difference, or a long trip driving at 65 mph versus 55 mph). Using this lets me see how gas prices have fluctuated, and where the better gas stations are that do not require me to drive out of my way. It also convinced me that 100 kph is way better than 118 kph (I learned to drive in Quebec, I loved doing 125 kph but not any more). You can also record all maintenance in it. Remember short trip driving is much harder on a car than long tip driving, it is all cold, and the alternator doesn't get to recharge the battery well. It may sound like a lot of work, but it isn't - I just fill everything in when I get gas, and run the numbers when I feel like it. You might want to also list what the trips were for - just work, or errands, or something else - either in the car book, or on a notepad in the house. This would let you see what you are using the car for. And a thought - you have a large vehicle for a one adult, one child household - is it because you need the space for the dogs? If yes, hold off on a replacement until the dogs are at the Rainbow Bridge - then you will need a much smaller car.
Son and father - given what you have written about your ex-husband, it sounds like you have done your son a favour by having him grow up without a toxic father to deal with. Living in a single parent home with a parent who loves him is much better for him. So please do not automatically think you have to "make up for" not having a father, and get rid of "guilt spending". If you don't believe this, head over to Captain Awkward's web site some time and see how many people are traumatized by their toxic parents, to the point that some have cut their parents totally out of their lives. And Disney - yikes. My DD went twice to the one in Florida, and barely remembers the first visit. She remembers the one when she was 7.
And as someone who is in a house (all by herself) because she has the dog and loves gardening - unless you love gardening, it will be a chore. All you really need for the dogs is enough yard for them to "exercise" in. Real exercise is walks, chasing a doggie Frisbee, things like that.
Tracking money - there are two schools of thought here. One is cash - it hurts to spend, but if you don't track it, it evaporates. If you can get it in the US, I strongly recommend watching Gail Vaz Oxlade's 'Till Debt do us part. She does cash budgeting very well. Otherwise, using a debit card (one where you are not allowed to go into a negative cash balance in the account) and Mint/YNAB will let you see exactly where your money got spent. Both ways work, it depends on the person which is preferable.
Please don't knock the "little things" suggestions. If you reduce/eliminate a recurring cost it is done for good, and the savings accumulate. Go for the "low-hanging fruits" first, since they are by definition easy to implement, but if you can keep major costs (like housing and transportation) down, that saves you a lot for a long time.