Assuming that the chain and sprocket sizes match, being able to pull the chain away from the rear sprocket when the chain is snug is simply a result of the chain being excessively stretched. Since you have replaced the rear sprocket and still experience the same problem, I would guess that the front sprocket has excessive radial run-out (sprocket is out-of-round). Many years ago, I was about to leave on a motorcycle trip and decided to alter the final gearing to improve gas mileage. The bike was tuned and geared for performance and gas mileage was low as a result. Anyway, I replaced the front sprocket with a larger one, adjusted and lubed the chain, and checked rear wheel alignment; good to go. I always checked and lubed the chain during each fuel stop when on a trip; first fuel stop, the chain was quite loose. I wasn't sure what was going on, but I adjusted and lubed the chain and carried on. Next fuel stop, the chain was loose, again. I then knew there was a problem, but there wasn't much I could do about it at the time other than adjusting and lubing the chain, again. With a few more adjustments, I made the 600+ miles to my destination. Obviously, my chain (an expensive #530 endless O-ring chain) was shot. Since the problem started with the replacement of the front sprocket, it pretty much had to be the problem. Bought a new front sprocket and chain (the rear sprocket looked fine, so I just flipped it) and installed them. Did a good bit of riding over several days and was confident everything was fine before making the return trip. The bad front sprocket looked okay, but a dial indicator said otherwise. Back home, I returned the bad sprocket and the dealership reimbursed me for the cost of the sprocket and the chain it ruined (I knew the owner and had bought the bike new from him; he had the sprocket checked and was eager to please a good customer).
Prop your mini's rear wheel up off the ground; rotate the wheel a little bit at a time until you find the tight spot in the chain (nearly every chain drive has a tight spot, a loose spot, and the rest is somewhere in between; always adjust chain at tight spot); using a paint marker, put a mark on each sprocket at the point farthest from the other sprocket. Repeat rotating the wheel a little bit at a time and checking for the tight spot; locate the tight spot multiple times; if the front sprocket is in the same position each time, the front sprocket is the problem; if the rear sprocket is in the same position each time, the rear sprocket is the problem (the sprocket may be okay but not mounted properly). If your sprockets seem to be good, I would suggest installing a spring-loaded tensioner on the bottom run of the chain so you can run some slack in the chain.
