Every other day I've had to jump my car battery.

The vibration during braking could be warped brake rotors. That is not serious and is likely not related to the dead battery. The dead battery is due to a defective battery, something is draining it, or it is not being recharged after starting the engine. Logic would dictate something is draining it since the rest of the system tested okay but there's more to the story. AC Generators are often intermittent due to worn brushes so any testing has to be done while the problem is occurring. The generator could work during the load test but fail a few minutes later. Evidence of that would be the "battery" warning light turning on, and / or head lights dimming and the heater fan slowing down. If you have a "Volts" gauge on the dash you would see it drop too. That's when you would have to jump out and measure the battery voltage while the engine was still running. It must be between 13.75 and 14.75 volts.

Batteries are rarely intermittent so if it tested okay, it most likely is. The exception is if it is covered in battery acid condensation.

That leaves a drain, and that battery acid can cause "self discharge". Don't suspect that if the top of the battery's case is clean and dry. If no other cause is found up to now, you can disconnect the negative battery cable, then reconnected it days later and see if the engine starts. If it does, a drain is the cause. If it does not, the battery could still be the cause of the problem. Because of the many computers' memory circuits, there will be a small constant drain. A tired, old battery may be able to provide a short burst of energy to run the starter motor, but it may have very little reserve capacity to run those small loads for more than a day or two. You can find evidence of that by first driving the car a good ten to fifteen minutes to be sure the battery is fully charged, then you stop the engine, disable the fuel system, then see how long you can crank the engine before the battery dies. You never want to run a starter motor for more than about five to ten seconds without letting it cool down for half a minute, but if you can only do that two or three times, suspect the battery. Another thing you can look at is the charging meter on a battery charger. If your battery is nearly dead, when you turn on the charger you will see the current remain low for a few minutes before the battery STARTS to take a charge, then the current should remain around 15 - 20 amps for up to an hour or more. The current will drop down to around 5 amps when the battery is fully charged. If that happens in just a few minutes, the battery has lost most of its capacity, even if it did test good on that 15-second load test mechanics perform.