In most styles of omelette vegetables are optional. The obvious exception is the Spanish tortilla, where sliced or grated potato (and possibly onion) adds strength, but that's cooked more slowly and not turned.
Tomatoes in particular are tricky, as they're so wet. The same would apply to courgette, for example. Large quantities of veg also make it harder, as the egg will be too deep to cook through, so you end up breaking it up. You can try finishing it off with top heat (grill/broiler) but I've never bothered as it means heating up another appliance.
Cooking small quantities of veg in with the egg is possible for some things (onion, mushroom, pepper, for example, probably started before adding the egg) but it's not easy to get it cooked just the right amount, and too much will lead to collapse.
Instead, what I do for larger quantities or wetter veg is pre-cook the veg by frying in the same pan, then drain and reserve. After that I cook the seasoned egg into a nice flat omelette, return the veg and any other fillings such as cheese to one half, and fold, for a filled omelette. This way you can put as much or as little veg as you like. You can also microwave the veg.