so you are travelling with the house battery in your car, then you connect the car to the home ?
where is the refrigerator ? in the car ?
because when arriving at home, the beer will be warm, since the battery was with you in the car, it can not power the refrigerator at the same time (unless solar was able to do it). But then i do not see the point to have a Lv2424 all-in-one since it is supposed to work only with a battery connected. and then you loose all the home solar power since you were not able to store it into batteries.
I think you have to review your workflow
you need 2 sets of batteries on in the car, another one at home.