Inner tube valve fit/pumping question
To buy time, I'd attempt a patch.  Since the damage looks bigger than a commercial patch, I'd cut a larger piece from an old inner tube, and make one.  Downside, any other part of this  old tube could fail in the same way.  Changing tube with a load-on is challenging.
When you do find a supplier, buy at least three tubes, two for trailer, one for spare and any more to store at home.
My searching shows they are available, but 1.75 is rare and 2.125 is more common.  You could stuff this larger tube in your existing tyres, and they would be a little more robust due to less stretch, but harder to mount without pinching.   So consider your existing tyres and whether its time to replace them with 16&quot; x 2.125&quot;, or more.  3&quot; seems to be a common size too.
Which leads to - Have you ever weighed your loaded trailer?  Get a bathroom scale and in turn put it under each wheel and the drawbar.  Sum the three weights, and that's your total.  Guessing you carry 50-80 kg in there, so a wider/stronger tyre will help.   The recommended max for my trailer is 55 pounds/25 kilograms, but I've carried 100 kg of UPSs successfully.  More-robust tyres certainly help !