help me understand

Gender Identity and Sexual orientation are two different things.

It sounds like your cousin has come to terms with the fact that she feel uncomfortable being male, and would be happier as a female. This is absolutely fine, and the fact that she's a lesbian has no impact on gender identity. She's attracted to females, but also desire to be female herself, and you should respect that because it's probably hard enough on her just trying to find comfort in her own skin.

 

Well I think two things in your situation.

1.) You need to talk to your cousin. Tell her that you don't fully understand, but that you are really trying to understand and respect her decision, and that you'd like for her to tell you about it and how she feels. It might be a bit of an awkward conversation, but in the end it could bring the two of you closer

2.) For your kids. I'd suggest that you get together with your cousin once you've gotten everything sorted out for yourself, and the two of you together can try and explain it to them. They're young, they'll understand.

 

Well, I think that the main thing to take into account is that, as odd as it might seem... nothing really changed with who your cousin really is. You just didn't notice who she really was until now because she kept it hidden.

So, when your cousin was born, she was assigned a male gender because that is in fact what her body is like. Yet, over time, she came to notice that something was seriously amiss.
For example, while I may be gay, I am pretty much purely a guy. I act like a fairly stereotypical guy, I feel at ease calling myself a guy, if you show me a line of boys and a line of girls, I'll join the boys line without a second thought. It just feels natural to do so. I'm assuming its pretty much the same for you.
Yet, transgender people like your cousin don't have that. Everyone is telling them that they're a boy, but they feel like a girl. They feel like acting like a girl would be more natural, that dressing like a girl would be more natural, that if they could join a line, they'd be so much more comfortable joining the girls line. In the same way that "feeling like a guy" is natural to you, "feeling like a girl" was natural for your cousin. Except that her own body just happened to be a male one.

And she might not have told you before, but I can all but guarantee you that she has had this issue for most of her life, until it finally made sense to declare herself a girl and tell all the world what she really feels like.

Then there's the whole sexuality thing, which is really a different issue. She just found that to her, romantic (and erotic) feelings for girls are what comes natural.
Of course, beforehand your cousin presented as male, so it was deemed "natural". While now it might seem odd to present as a girl and still be interested in girls. So essentially, what she's telling you is that she only pretended being a boy, but her interest in girls was never false.


And I think that the above should inform both your questions to her and how you tell your kids (if you choose to do so). If you want to discuss with her, try to focus on "how was life for you beforehand and how is it now. How did you feel back then and how do you feel now?".
Try not to focus on the "but you have a penis!". She probably notices that multiple times a day already. As well-meant as objections from your side may be, she probably has thought of them all. So keep focused on getting information and gaining an idea of what it's like being TG, instead of suggesting you know better who she is than she knows herself.

Similarly for the kids. If you tell them, you could just tell it like "most of the time, boys get born with boy parts and girls get born with girl parts. But in the case of her, something went wrong and she was a girl born with boy parts. But she really is a girl, even if she has a more heavy voice". Kids are usually more broad-thinking than we sometimes think. Of course, you might want to consult with your cousin if she feels OK with that explanation.

Last, but very much not least: it's not always easy understanding these things. I had the biggest problems understanding things like being gay (and I say that being gay myself )
Making an honest effort is already a good first step, so I must commend you for it!