In the UK the market leading solution is the child seat - I reckon that one trailer is sold for every fifty child seats. Cost obviously is a factor in this plus the fact that trailers are a slow seller and many shops do not have the floor space for them.
The situation your sister is in is not a new one, plenty of people start cycling with their kids having not been on a bike since secondary school. Therefore I don't think it is necessary to be defeatist with the child seat.
The child seat, particularly the Hamax ones have suspension built in and offer a superior ride to that offered by a trailer. The view is better too. Okay there may not be UV protection and a cover from the rain but there are pros + cons to each solution.
A two-year old on the back of the bike is a considerable weight, however, harnessed in this is a fixed weight, it is not like riding a tandem.
A Hamax childseat bought off 'craigslist' or out of the local paper can be wiped down and made perfectly serviceable. If it does not work out it can be put back on 'craigslist'. Because children grow there is a healthy second hand market for them.
In the park you could go out with your sister and the childseat and instead of having the two year old in the seat you could have an improvised 'crash test dummy', e.g. a couple of bags of shopping, e.g. a growbag or small sack of potatoes. If she can ride confidently with that weight on the back then she may feel confident enough to go out with her two year old child.
Although the weight at the back makes the front wheel light it will also make the steering feel easier/less twitchy. So it is definitely worth a go.
As for a trike - have you tried riding one recently? They are a nightmare because you have to steer rather than lean. I find them terrifying to be on because they feel so weird.
Getting back to the childseat, the Hamax ones come with a bracket that is easy to get a spare, pop one on your bike and you can swap the childseat from one bike to the other when those hills get a bit steep.
You can also pop a bike with childseat onto a bike-carrier on the back of a car.
This cannot be done so easily with the trailer option. Be open minded about the childseat, give it a go with a 'crash test dummy' and take things from there.