Product recommendations are usually off-topic here, as the availability of products depends on the region, so I'll define some guidelines and give some examples.
Generally speaking, what I commonly see around here (Central Europe, living in a street with schools) for this use case (short rider with kids) are compact cargo bikes with central motor with 20" wheels, like the Tern NDB/HSD/GSD, Trek Fetch 2+, Cannondale Cargowagen, Specialized Porto to take brands that are widely distributed. But these are not endorsements, and better local brands can be available as well. It's a booming segment. Note that some of the examples are expensive, but they are competing with second cars rather than regular bikes.
By compact cargo, I mean bikes designed to be loaded with luggage and kids with 20" wheels - note that only the "loaded wheel" needs to be 20", some have larger front wheels, which is positive for comfort and obstacle clearance. The benefit of 20" inch wheels, besides the compact side, is that it lowers the center of gravity, which makes it easier for shorter riders to control the bike when it is loaded - and lowers the height at which kids have to be lifted to be seated. Another when it comes to carry people of cargo bikes (in general) is that they are typically designed to carry bigger kids than what you can do on regular bikes: some have rear racks rated for much higher loads (generally around 50-60kg, the max being 100kg vs 25-35kg for normal bikes) and you install other kind of seats that the "conventional child seats", that can work even for adults. But that allows to fill up the gap that some have when kids are becoming to big to fit on a child seat, and it's still too early to let them ride on their own.
The central motor is recommended, because the alternative (motor in the wheels) doesn't handle very well hills and/or high load. Although, I have to admit a European bias here, where the limit for electric assistance is one third of the US one. So it's possible that a hub motor in US works as well (RadPower RadWagon, Aventon Abound).
For short riders a kickstand with two legs is highly recommended. Having a front rack is also important for utility purposes: it allows a better weight distribution when a kid on the rear seat, as items can be loaded on the front rack. If the budget allows it, an internally geared hub is recommended, as well as a belt drive instead of a chain (belts are virtually maintenance free).
For off-road, it depends what is defined by off-road, as paths in parks can be smoother than some roads. Compact cargo bikes typically come with wide-enough (55-60mm) tires that can handle rough surfaces - dirt, gravel, cobbles..., but not so well larger obstacles stones or roots. Most city bikes come with tires with light threads, that work well for that usage. The front suspension helps with comfort, but less than quality tires. True offroad requires a full-size bike, but that's probably not someone wants to do with a child anyway - and handling a full-size e-bike with a kid and some luggage is challenging for short/light riders.
