Do you have charge regulators in your unit for mains and solar ? Also your inverter sounds like it’s external to the tote also?
i have several lipo batteries, so i use the one external charger dedicated for lipo that plugs into the mains. it charges at 14.6v and can support up to 20 amps. all my solar setups have their own charge controller, so i have it set up where i can just go to any of my other setups and unplug from that battery and plug in the tote and charge away.
the inverter is quasi-internal...meaning that it is in the tote, but i have to open the lid and plug into it. i have the 280ah battery with a piece of plywood on top that i use to mount the bus bars, fuse block, etc. the inverter just sits on top of that and when i need it, i just open the lid and plug into the inverter. i would need more room inside in order to mount and wire in a mains outlet. i dont use the inverter enough to worry about it, but it is there and operational when i need it.
when you get a battery, read and check its charging requirements. i know the last few lipo batteries i bought were 14.6v and up to 20 amp. sounds crazy to me, but yes, these newer batteries are built to get charged very fast without any damage. i forgot the exact specs, but when i bought the special charger, it is supposed to charge the 280ah battery in 2-3 hours i think. whatever it is, i remember it was crazy fast
on all my lipo batteries, i wire in an anderson plug that stays on the battery posts and that way if i ever need to charge with the mains, i can just plug in the charger and directly connect to the battery without having to do any hookups and i certainly wouldnt use alligator clips to make a connection. when messing with lithium batteries, i want a VERY solid connection that has lots of surface area and wont get bumped loose.