Ulva is an excellent nutrient sponge, export medium and herbivore food. When it is vigorous and healthy, it isn't so fragile. But in low nutrient systems, like reef tanks, they don't get enough and fall apart. They prefer high light and high nutrients. So it may not be the right macro for your situation. You should diversify your macro selection to include macros that can thrive on lower nutrients, so you can get better performance in different nutrient levels. Red macros like Gracilaria are a good option.
If you really want to grow Ulva, and your display tank is too nutrient deficient, set up a small tank separate from your display system that you can give it all the light and nutrients it wants. Crank up the lighting and dose ammonia and you will have tons of it in no time.
You may be able to improve your situation in your fuge, by adding Iron. Iron is a trace element that plants need and it often gets stripped out of closed systems quickly. Try a marine iron supplement to see if that helps. It often does. I would try this first. You may find that your corals like it too.