I use a 43 # thrust electric trolling motor on a 12 foot Aluminum Duroboat (much easier to push than an inflatable except maybe a larger RIB). It will go about 3 mph reliably--and I have two golf cart batteries--210 amp hours. I would not attempt to go 1-2 miles with that rig. I use in for nature watching in a calm bayou.
If you get an inflatable on open water, you run the risk of having the wind/waves come up to the point that the small engine (even a 2 hp) might not be enough power to get the inflatable back to the boat--or kept it from being blow out to sea or some distance from a safe harbor. (this is from personal experience--I now use at least a 2.5 Hp outboard. There are a number of outboards which are 29 to 32 lbs. You talk about the weight of the trolling motor--granted these are light. But, the battery, with enough power to take you significant distance will be heavy--at least 45 lbs (a group 24, which is marginal for your use). As for re-charging--unless you have a generator which you will run some long peroid of time, you will have a difficult time keeping this trolling motor battery fully charged. For example, you will charge a group 27 battery at 10 amps--and it will take 6 hours to replace 60 amps.
If you want to go that several miles across the lake, get at least an 8 foot inflatable, and at least 3 to 4 hp outboard for safety.