How awful. I am never one to excuse sexually inappropriate behavior except (Yes, I see the incongruity of saying that!) when there seems to be a dementia component. If he has moments of lucidity (which I assume he does because you say he is hiding his behavior in some way - at least not admitting it), then I think you can say something to him. Not that it will change his behavior, but you can explain that he is not allowed to be with her since he "forges" that a closed door should stay closed and that privacy is privacy. Then don't expect I'm to remember it 10 minutes later.
I agree to absolutely support your daughter in speaking up and telling you. As others have said, explain that some older people (not all) get a condition that messes up their brains. I wouldn't call it a "disease" or "sickness" because you don't want her to think it's something she can catch. But do tell her that someone is going to guard the door every time she goes to the bathroom. I think you also have to take precautions in her bedroom - if you still have a baby monitor, that's one way, but I'd more likely put her on the floor of your bedroom for the rest of the visit if you aren't planning to ship him home early. Borrow an air mattress from a neighbor if you have to, or pick something up at the local Target store.
I am really upset that your aunt put a frail person on the plane by himself - I'm sure she needs a break, but still. I would think you should hire someone to accompany him, unless someone in the family can fly out and back, which I realize is tough at Christmas, and expensive.
If you have to save up to buy his ticket back, then you don't have much extra cash now, so it may not be possible for you to hire a home aide to sort of "babysit" him. There are elder services that provide non-medical care - I had people when my mother broke her shoulder and was very unsteady with her arm in a sling. She had bad balance and was falling again and again. She didn't need nursing care, just someone to do a little simple kitchen stuff and help with bathing. Many of them are personal care attendants or students working on their nursing degrees, but they are much cheaper than nurses and physical therapists who have more training. I don't know if you can find someone around the holidays but it's an option. For reference, we paid $23 an hour, some of which went to the agency and they paid the person around $16 I think.
I think you should write a letter directly to his doctor and explain exactly what happened. His doctor can't divulge info about him to you, but can (and will) certainly read what you have written. I think you can consider contacting the VA yourself, but you might also ask the doctor if it's necessary to report this to either Elder Services or CPS in your grandfather's home state. SOMEONE needs to make sure that he's not with any other children, especially girls. It's not clear to me that your aunt is taking it seriously enough. Maybe she is, but you should do your due diligence here, especially since this occurred in your home. It's more influential than sort of "playing telephone" by having your aunt relay your info. Be very specific - maybe list bullet points, one for each incident. Say more than "he was inappropriate" or "he was secretive" - be detailed in what happened, what you said, and what he said in response. The doctor will want to know what your grandfather's affect (appearance, expressions) was as well as anything he said or didn't say. That will help the doctor ask him more questions and evaluate for dementia as well as call in whatever services in their town/county are appropriate. I think you can consider calling Elder Services in his town too, to see what's there and what your obligations are. If you grandfather should ever wander off, you really want someone to know that he has been inappropriate before. It's possible that the local police should be notified too, not that they will arrest him or anything, but in many smaller towns, the police are a tremendous resource if an older person goes off the rails. If Grandpa doesn't have an ID bracelet with his name, address, medical problems (diabetes, heart, whatever), doctor's name and your aunt's name/number, please get one. My son and husband wear one all the time because they are runners who never, of course, carry a wallet or license when running. There are many that are "fashionable" or at least nondescript, and they don't look like purely medical bracelets. Road ID is one brand, and there are others.
You are going to have to involve the rest of your family, including your sons, in staying with your daughter and standing outside the bathroom door, every time she has to go. And I realize that a 4 year old isn't going to remember to say, "Hey, everyone, I have to pee - who wants to go with me?" Put a little travel video game or something for a person to do while they wait for her to finish. You cannot put a 4 year old in a locked bathroom or bedroom - you must be able to get to her in case of, say, a fire, and you cannot have a locked door between you that you rely on a child to open. If your grandfather is really frail and has a weak grip, you could consider one of those childproof doorknob covers on the outside of the door, if (and only if) you secure it so he can't get it off easily. That way you and other adults can get in if necessary, and she can easily get out by using the plain doorknob on the inside.
Finally, I know this changes how you feel about him. Your long-held view of him, your admiration, has changed forever, and there's a loss of your own innocence from childhood that goes along with that. And of course you feel sick and have a case of the "what ifs" regarding your child.
Good luck - while being furious and vigilant, I hope you can have a nice Christmas and be comforted by the warmth of a good grandpa for so many years until this happened.