You could do what RVs do: have a separate "house" battery that's charged by the car's alternator while driving. Then connect an inverter at the battery and run extension cord from there. You'd have to look at how much power your equipment will use, and how long you'll use it between recharging. You can probably run your equipment off a 2000w inverter. You may need a 200 Ah battery in order to get through the day, but I have no idea how far you drive to recharge the battery. All of that might cost more than new equipment. You don't want to run off the car battery as it could be dead by the end of the day, unless you leave it running.

Have you considered a generator?

You are going about it in a roundabout way - doing and creating things that won't work well. Almost like a Mr. Bean skit. You would have so many multiple of hundreds of dollars to get a cumbersome setup that still hampers your work. The inverter with enough startup amps (you start up both the trimmer and blower dozens of times) basically negates this whole setup.

The better, cheaper, and most efficient solution is to buy a simple Black&Decker cordless string trimmer/blower combo kit for $119 at Home Depot, or a better B&D kit (2 larger batteries) for $124 at Menards if you are near one. Plug 1 battery to charge at the house while you work, then switch when the task changes. Or buy a $5-$18 cigarette lighter inverter just to charge a battery while you drive between jobs.

Or look for used ones on social media. I just sold a 2-cycle trimmer for $5, and have sold the exact B&D kit for $75.