traeger Jr., a grp 27, an inverter. What's the best recharge

I agree with Mexico, take all 4-batteries, it's better to have them & not need them, rather than need them & not have them, (but, I'm pretty sure you will). Depending upon the size of your Generator & as you stated, running it each morning. I think I'd connect the Genny to the converter, charging the coach batteries & separately at the same time, connect the Black & Decker to the grp 27 batteries.