Yeah, mozz is a cooking not a melting cheese. It's already kinda melted and stretched, so there's a much bigger hurdle to get it to loosen up.
Milk helps, but starch is critical; you can't have a stable cheese sauce without milk and starch -- or citrate (and related bits, hexametaphosphate etc.) to make the proteins unlink and get a nacho or process-cheese texture.
Avoid excess heat, too; heat almost inevitably "breaks" sauces. It's tricky, because you need to simmer but you need to stay below boiling. Boiling is easy, it's self regulating, but you need juuust enough heat otherwise, and perhaps enough stirring to encourage evaporation (cooling), without getting away from it too long and it starts bubbling.
Cheese you can usually get away with overheating as long as it stirs in and starches block it from glopping together, but it might still end up grainy or something. Or you might need the heat to get it to melt, not entirely sure, but it can be hard to melt some cheeses -- hard ones like coarsely shredded parmesan, or cooking ones like mozzarella.
Tim