So you guys fucked things up for your 9 year old niece. And now you want to keep this child and her guardian from ever finding out that you fucked things up for her, while simultaneously erasing all evidence of a massively popular leaked video clip.
I think you need a different approach than the one you're taking here. You all need to learn from this experience. The point of focus should not be getting people to feel bad relative to their culpability, and or minimizing the fallout of hard feelings you anticipate when you tell people that you fucked things up for them.
Your approach seems to be based around keeping as many people in the dark about this as possible, including the rest of the internet. Kind of difficult to do that when things, like they have at this point, have spiraled entirely and permanently out of your control.
Tasha needs to know. This means that Tara is going to have to know. The approach you should take is by approaching Tara and telling her, ASAP. Let's review this part:
Tara had serious concerns about it getting put on the Internet and going viral.
...aaand that seems to be why you don't want to tell Tara -- because she was right, and exactly what she was worried would happen did happen. Keeping her in the dark will do nothing for Tasha, it will only keep you guys from getting some negative response from Tara.
That's terrible reasoning. Get some backbone, tell Tara about the mistake, and deal with the emotional dramatic fallout. She gets to be upset. As for the first two below she should speak with an attorney, but she was probably also right about the last one on the list:
She was worried that she could get charged with a crime, Sasha could get in trouble, or that Sasha would be humiliated.
Sasha is probably going to be humiliated. You know, because you guys were getting your chuckles out of something she had already said she was embarrassed about. And your clumsy sharing of it means that now millions of people have seen it.
You all are going to have to own up to some culpability. Obviously you don't hate your niece and weren't trying to harm her. But her being embarrassed about a video of her means that she, even as a kid, should have her wishes respected. In this case, however cute you thought it was, you should have deleted it.
If you're lucky, by now Sasha has moved on from being embarrassed by it and will consider it something other than a lasting mark of shame. But that's her process to go through. Keeping it from her will just delay her from getting started doing what she's going to need to do to get over it.