My children (almost 4 and 2) are a bit scared of the stove as well, and we've been working on this slowly.
Currently, the main things they do involving the stove are two things:
- Adding chocolate chips to pancakes after I've placed them on the griddle
- Stirring macaroni in boiling water in process of making mac+cheese.
Both are things that they really enjoy, so the desire to do it overcomes their fears most of the time - even to the point that the older one briefly touched the griddle and managed to be okay coming back to put more chips on after we cooled his hand down. The idea here is simply that we're getting them comfortable with being around the stove, building confidence and tolerance, sort of like teaching swimming by starting with just being in the water not doing anything for a while.
With the stirring, he uses a really long handled spoon/spatula, which allows him to be quite far away from the pot and very safe in terms of not getting splashed. Being on a stable and tall stool are also key; being able to look down at the pot is important as it gives him a good sense of control (and is safer to boot).
A lot of what we do still of course is non-stovetop work; mixing pancake batter by hand or in the stand mixer, mixing smoothies in the blender, adding liquids to things. I like doing these kinds of activities, in part because I hope they will encourage them to be interested in cooking and in being involved - and then lead to wanting to do more on the stove. Of course, it sounds like you're already mostly there.
Finally, you might consider getting a hot plate or an electric griddle for her to practice with. That gives the great advantage of being able to be placed at her height, as well as being much smaller in size. The griddle in particular is nice because it means you don't have a pan to manage - the griddle is the pan. Thus no risk of knocking it off. It can be set to a fairly low temperature (which makes eggs easier, anyway!) and since most are non-stick you can avoid the risk of oil splattering (you may want to use a bit of oil, but much, much less, though of course you can use a non-stick pan for the same purpose).
Something like a small Presto-type would work, for example; usually available in the $20-$25 range and nicely small for a child. They also usually have a temperature control rather than just 'medium', which makes it a lot easier to cook consistently in my experience.