I've done a lot of dodgy things in my time.. But I've never had radiator hoses pop off. Have you had the cooling systems operating pressure checked?

Unless it's physically getting pulled off from engine torque or something.

You can get some hose sealant/glue stuff (I've used it), but then it's almost impossible to get the hose off in the future.
Remember that most modern car use pressure clips, not even hose clamps to keep the radiator hoses on. So I think there is something else wrong.

edit: so I see from the photos that it's very likely the hose diameters are different on the radiator, and on the engine. You might have to use parts of 2 different radiator hoses, and machine up an adapter between the 2 diameters.