Those are standard folding wheelchair hubs (the wheelchairs fold, the wheels pop off easily), and they're really not designed to work in bike trailers. Folding chairs are typically used at low speed and for comparatively short distances. Despite the weight of wheelchair users, in practice those axles will bend on a bike trailer at much lower loads than you would expect because of the dynamic nature of the bike trailer. You just don't see people riding wheelchairs off curbs at 30kph, or through potholes at 50kph... both things commonly done with bike trailers. So be careful or expect the bend axles.
You should be able to find higher-quality wheelchair hubs, but I have no idea how or where. What I suggest is measuring the axle diameter because I suspect it will be 10mm, which is a standard bicycle size. If it is then you should be able to get any standard bicycle hub that uses cartridge bearings (like your current wheels do) and fit the axle you have into them. Test fitting should be straightforward, so I would take a wheel and axle with you when you visit bike shops.
Depending on how committed you are you could just rebuild the wheels with better rims and spokes, or you could replace the lightweight pop-off axles and wheels with something stronger. That might, however, just shift the point of failure into the frame of the trailer. So you'll need to think about how strong the trailer and hitch is, and whether bending the axles really is a problem for you.
In my case I looked at those axles, thought "that's really cool", read up one other people's experiences, and decided not to go down that route. My current trailer has a 20mm through axle that runs right across the frame, but I also carry more than 100kg in it on a regular basis.