Couple thoughts from me.
First, congrats on getting things together! Adulting is hard, taking practice, and is a process. You are making progress, so be proud of that.
Second - your "use for whatever money" - oil changes aren't optional. They should be included in your budget. The unaccountable money should cover things like toys, clothes, treats, occasional entertainment, etc. Sounds like you didn't define your budget to include some things that you should have and that's why the "free" money is so big. Go through that category again and figure out what should be classified elsewhere, then you'll have a better idea of what the "free" money really is. Example: Annually, I pay 2 professional memberships. I don't have a separate category for this, but I also don't include this in my spending money. So I have an "Other" category to account for those types of infrequent things.
NY Times online - you might check your local library. Mine has some pretty cool looking services that I'm just digging into. I can get the digital Economist for free through the library for example. Free = good!
The 2nd dog - he's made huge progress, yay! He just has problems with other dogs? There's plenty of dogs out there like that, it's on you to control him and prevent issues. With past abuse, some things really can't be completely eliminated. Time and TLC will go a long way. But he may never be comfortable at a dog park, and it's on you to recognize that and not push too far. Make sure you can control the dogs, recognize when things are too much and get them out of the situation, and continue the training on your own. You won't need professional help long term, it's more of a temporary thing to get the dog started and train the humans.
Regarding the meds - ask your vet if there's anything you can do to reduce costs. Maybe a different med is equally effective but a cheaper. Sometimes they get rebates, etc from manufacturers. Can't hurt to ask.
Seconded on finding a less expensive but still quality food. Per my vet, the gold standard is feeding trials. Meaning, they've actually fed animals that food over a period of time and results were good. Many of the newer "fancy" foods don't have those - they're expensive and time consuming to do. I just switched my cats from Blue Buffalo to Purina One. About 1/2 the cost I think, and its a good quality food (that the cats actually like better, go figure).
Your vacations are staycations. Do some sightseeing close to home. Relax, sleep in. Catch up on your favorite shows, crafts, whatever. Throw balls for the dogs until they're worn out.