There's no such thing as senseless violence, according to the one who commits it. Characters who kill or torture without at least an internal justification are crazy, not evil. You don't have a reason to kill people in the party or at random, so you don't. This doesn't make you nonevil.
Also remember that just because you're Evil doesn't mean you're a villain. Many Evil characters have no ambitions higher than their own survival and/or comfort; they don't aspire to great power, nor to purge the world of the target of their hate. They're just trying to get by, not so different from the rest of us.
The traditional list of Seven Deadly Sins was originally compiled not so much as a list of inherent sins, but a list of reasons that people sin. This makes it a great source of motives for Evil characters. I prefer to expand the list to nine, adding Fear as Wrath's twin in the fight-or-flight reflex, and Despair because it was actually in the original list; Sloth replaced it later.
Avarice: The key to happiness is having things. I will have it all.
Envy: I deserve it, not them. I will have it from them.
Gluttony: Pity those not at the top of the food chain. I will never be in that position.
Lust: I want to do it all, and I will let nothing get in my way.
Pride: I must be better then them: so much so that my superiority is never even questioned.
Sloth: I just don't want to do it. Let them do it for me. If they refuse, make them do it for me.
Wrath: They will never hurt me again. I will punish them for what they did, and leave them unable to do it to anyone else.
Fear: They must not be allowed to hurt me. (Note the lack of an again here: this is one of the big differentiators between Fear and Wrath, but it can make a huge difference in the character).
Despair: I just want the pain to end. Giving it to others helps.
Also keep in mind that these are core motivations. Any one of them will need to be elaborated upon. What is it? Who are they? How does the character plan to achieve this goal? Also worth noting is the lengths that your character goes to to hide her motives. Evil characters often prey upon one another's weaknesses, and while Wrath-type characters might not worry about seeming weak due to their motives, Sloth-type and Fear-type characters likely would. These folks are likely to construct a facade, often but not always based on Wrath, as a matter of posturing.
Your character sounds like a Wrath-type, with a focus on the undead. Because her main focus is on something that is not so amenable to the survival of humanity in general, she can get along decently well in society, and even be a very useful sort of person to have around. Some might even mistake her for heroic. But she has a twisted fight-or-flight reflex: any slight or injury, real or imagined, runs the risk of touching on that trauma, for reasons that make sense only to your character (if they even make sense to her). She might lash out disproportionately at small threats, or even against things she mistakenly believes to be threats, but are not.
So
All dragons aren't the same, so you'll see variation - especially with creatures as powerful and already-unique as dragons.
You should be comfortable making this up yourself. Information on stuff like that tends to be spread across many books and is often done by example (oh look, a mated dragon lair) as opposed to a diatribe on dragon mating.
Having said that, apparently you have Dragons Revisited but haven't read it and want us to for you? It has such information, varying by breed. For example, black dragons:
Territoriality
Through careless pogroms and
occasional genocides, black dragons drive off or slaughter
all living things surrounding their lairs, creating wide
swaths of barren swamplands.
(among other details)
Mating
The slinking “loser” is the female, who slips away to return to her
own domain and begin the process of readying for her eggs,
letting the male attract attention to himself while she nests
in safety. After mating, the male has no more connection
with the female or her eggs, and if ever again the two meet,
they treat one another as bitter and hated enemies. Females
can lay eggs roughly a dozen times in their lives, and every
time they do so it is with a different male partner.
Whereas e.g. brass dragons tend to be nomadic. They go into pretty specific lair detail on all of them, but not dragon-sex-and-mating detail, you may need to DIY until the Book of Dragon Erotica comes out next year. Just by plain example, most dragons they depict are solo, but in e.g. Dragons Unleashed they refer to the white dragon Sjohvor saying, "Nearly 900 years ago, Sjohvor had a mate with whom he shared his lair." So it's not unheard of, but seems to be rare.
Best Answer
By canon, as your question asks, nope.
First we'll define the word canon so we're clear about what we're discussing as it applies here, I'll leave out definitions that don't apply:
Canon;
a general rule, law, principle or criterion by which something is judged; or
a collection or list of sacred books accepted as genuine (or the works of a particular author or artist that are considered genuine)
With those definitions established, I'll be citing the Monster Manual for 5th Edition, which is based upon the Forgotten Realms setting.
The pertinent reference comes from the Monster Manual on Pg. 86 under the heading: Chromatic Dragons
This section covers the instincts that govern a chromatic dragons behaviour. I'm not going to bother pasting it here because the title alone sums up their drive, and the text simply expands on it.
The following is where alignment comes into play.
On top of that, the main header on the page titled Dragons also covers this pertinent bit (emphasis mine):
So, by canon alone, no, they can not be converted to good. Basically, it's like trying to convert a demon or devil. You could let them do it, you're the DM. Consider what the nature of the creature is though. Is it likely to be successful? What kind of problems are they going to experience? How are they going to deal with the backlash when the dragon eats it's first person or destroys a farm with it's breath weapon?
A good resource used to be The Draconomicon, however it doesn't translate well to 5th edition because it uses AD&D numbers, feats and skills. You'd have to do a lot of work to tidy it up, but there's actually a section on rearing eggs on page 13.