Looking at your second picture, with the set up I described, you will remove every thing from the tank. You will replace everything with larger parts. I will go with the assumption that you have a 1-1/2 inch threaded outlet on the small tank that you will be working on. (It could be 2 inch though, you will need to measure).
I will put links to everything in the order I described. I will use Home Depot and McMaster Carr for links and descriptions.
pipe nipple
McMaster-Carr
ball valve
McMaster-Carr or
McMaster-Carr
quick disconnect (hose coupling) 1st half
McMaster-Carr
quick disconnect (hose coupling) 2ed half
McMaster-Carr
hose barb---you can get the quick disconnect 2ed half with the hose barb as the way to attach built in.
tubing
Watts 1-1/2 in. I.D. x 150 ft. PVC Flat Discharge Hose-RCDR - The Home Depot
I would also put a fitting of some type on the end of the hose where you put it in to fill the large tank.
for the house hook up
Quick disconnect (hose coupling) 2ed half---see link above
Step down reducer (low pressure bushing) 1-1/2 inch to 1/2 inch
McMaster-Carr
1/2 inch pipe nipple ---See link above.
I used manly McMaster Carr for links because I found out Home Depot does not carry 1-1/2 pipe.
Also, PVC pipe can be used instead of Galvanized Iron pipe if you would want to go in that direction. That would be a choice you would need to make.