Oy, such frustrating behavior, I agree. My husband's family is very much like that - we go out to dinner, & I'm the only one not looking @ a phone. Some of them "tune out" while others are looking up stuff to show each other.
However, what you are doing is also frustrating - "putting her off" seems rather passive aggressive to me.
I love Wild Woman's suggestion - touch it & pay, literally! But that really only works for a girls night out dinner. It sounds like you would like to spend time with your friend, but only if you can SPEND TIME WITH HER. Right?
So, let her know that. Say to her "Julie I probably should have talked to you about this a while ago. But better late than never, & I don't want this to be an issue that comes between our friendship, which I treasure. I'd love to spend the week with you. But I really struggle with feeling like I'm competing for your attention when you are always checking in with other people on your phone, etc. I'd hate to have you come up for a week, & then feel resentful the whole time you are here, so I want to talk to you about it ahead of time"
And then, give her a chance to respond. I don't think this is a reason to toss away a friendship. Friends are like spouses - you both change over time, & communication is the key. A good friend is worth keeping that line of communication open, being honest & growing together.
When you talk to her - make sure it's to let her know that you want to spend time with her, & cherish your friendship, not scold her for doing something she may not realize is even an issue. As you said in your post, she is sharing her text & FB convos with you - maybe she thinks that it is OK (& for some people, it is!) because she's including you in what she's doing...
T.