My daughter and her friends almost never put her Barbie's away clothed.
It never occured to me there was anything weird about it. She had so many dolls and so many outfits, my main rule was that they all had to be put back in the case she kept them in and not scattered all over the place. There's not a lot to see on a naked Barbie so I don't know that I would be concerned about that part.
My kids are 10 years apart so I always had kids of all ages at my house. We lived in plenty of places where there were literally only two families with kids in a neighborhood and kids will usually like to socialize with each other or just have somewhere to go for a visit. Looking back at my own personal experiences, I would have to say that an age gap itself was never really a concern.
You say that the girl lies though. And the whatever they play is a "secret" thing...I wouldn't like that either.
I was always a pretty blunt mom and it sounds like you have talked to your daughter about keeping secrets, etc. This is something ALL children need to learn and understand and it's never too young in my opinion.
Next time the girl comes over, I would just say that you want them playing in the living room (or wherever) and then you can non-chalantly keep an eye on them. I know other moms mentioned putting baby monitors in the bedroom, but I would be more proactive about it I think. At least so you can get a sense of how they interact, how they play with the dolls, if there is a lot of whispering going on, if the girl continuously wants to play in the bedroom even though you've said you want them playing where you can see them.
A). If nothing weird is going on, they will be happy playing wherever you tell them to play.
B). You won't have to wonder what's going on or worry about it because you will be supervising them.
If the older girl asks why they can't play in your daughter's room, you can simply tell her that you've noticed they like playing with the Barbies, but they have been getting put away without any outfits on. You want to be able to give a 5 minute countdown so the Barbies can be dressed before being put away and you're trying to teach your daughter to be responsible with them. Or, "I'd really like it if you girls sat at the table and drew pictures or played with crayons and coloring books today." (Or sat on the floor and did puzzles or played Candyland or whatever). If the 10 year old isn't into it, she'll likely go home. It's your house, your daughter is 4, and even though girls of all ages can enjoy Barbies, there are other things to do too.
I know it sounds mean, but there have been lots of kids that weren't allowed to play in my kids' rooms. Period. It's not because they were really bad kids or anything, but they would come over and want to drag everything out, but when it was time to put things away, they would just leave and leave the mess. I was up front with them. I told them they liked to play with my kids toys, but didn't like helping clean up, so they had a choice of playing with this OR that, at the table or wherever else I said, but NOT in the bedroom and if they didn't like it, they could just go home. Some moms would make their kids get their butts back over or tell them ahead of time, "You better help and make sure whatever gets played with is cleaned up"....other moms had the attitude that toys will be toys and they get scattered all over, no big deal. Those were the kids not allowed in my kids rooms. Or my house at all if they didn't want to go along with my program.
I've come across more than a few kids, I hate to say, that were just down right sneaky. Or they'd put my kids up to asking for things that I clearly had already said no to. Trust me, once a sneaky kid knows you're on to them, they either do every single thing you say to the letter because they know you're watching, or, they know they've been busted and they stay away.
Just be upfront and watchful. Lay out the rules ahead of time.
No playing in the bedroom.
No putting the dolls away without outfits on.
No leaving without all toys being put away.
No keeping secrets about what you play.
That way, your daughter understands your rules and so do other children who come to play.
There may or may not be anything bad going on, but the 10 year old is plenty capable of understanding your rules and if she doesn't like them, she doesn't have to come over. She can understand that you're trying to teach your 4 year old. My honest hope, is that she would be willing to help you out with that in a good way. She'll be old enough to babysit soon so it's very important that she is responsible and conducts herself properly around younger children.
I wouldn't assume anything horrible has happened. But they can't keep secrets in front of you.
Best wishes.