you've got a 13 year old on tow in a fairly hilly part of the country, it's horses for courses. Even if money is no object, it's down to being practical. It's planning for the worst case scenario. E-bikes extend your space. What happens when you are tired and a long way from home?
SW has already talked about crank driven bikes. The only ready made crank driven bikes with throttle are from woosh. Lots of members have them, you can search the forum for their reviews, I don't have anything new to add.
BPM stands for big powerful motors. It's a class of geared hub motors, with a large 180mm core, much bigger, heavier and more powerful than the common e-bike hub motors that have 120mm core. Ezee make their own motors that have similar characteristics compared to the BPM motors that many members consider better than the BPM made by Bafang. Recently, there is a perceptible move toward the middle, 140mm compact BPMs. You see them on bikes made by Volt, Kudos and Oxygen. The smaller 140mm core packs in about 90% of the power of the 180mm BPM but performance at below 4mph is a bit lower.
The problem with all motors is the yield. That's the ratio between what you get out of the motor in term of mechanical power vs what the motor draws from the battery. An efficient motor is worth its money (and weight) if it's much more efficient at the time that you need a lot of assist. Small motors are not made for hills because their yield is abysmal at below 4-5mph. That's why I said horses for courses.