Don´t take it from me on the basis of my rep. or my supossed knowledge! I could be lying xDD
You already know of different sources and different opinions, now try to understand them. The reason why salt water animals are unsuitable as food for fresh-water animals is simple, the contents of salts and various elements are substantially different. The contents of iodine can be particularly troublesome as they can affect hormonal production (potentially ending in forced metamorphosis) if accumulated in sufficient quantities. Again, research this stuff if it really is troubling you, don´t just accept it because i say so xD
There is a lot of bad information out there and a lot of people who make claims about certain foods being suitable. Funnily enough, they almost never justify their advice they simply put it out there. As a rule of thumb, beware of people who just make claims but don´t justify them. If someone says "chicken is good for axolotls" and doesn´t justify it, be suspicious of the value of their knowledge.
About the alternative food item, it´s tricky as you have mentioned the four basic foods xD You can use "prawn", just make sure to use a species that is fresh-water. Crustaceans in general are excellent choices, nutritious, rich in calcium and also in carotenes. Daphnia, gammarids (scuds), fresh-water shrimp (red cherries are the most popular species), anostraceans, isopods (woodlice), etc, all make excellent choices.
If you could find a fresh-water alternative to prawns, they would make a good alternative. You can also culture some of those which should eliminate any problems that you might have had with live foods in the past.
You might also want to consider creating a partition in the tank in which you can offer bloodworms without fear of them being scattered around the tank. It´s worked very well for me in the past (not with axolotls, though) and for many other people.
Or you could work on your mother´s opinion towards earthworms xD