If she has been working on this problem for a while she has probibly used some of these or at least heard of them... But just incase...
I am assuming that from your post she was the sole center of her mommas last 2 years. And now it is being exasperated by the fact that there is another munchkin vying for the attention.
Has this girl EVER played by herself? As an Infant? Some people are hard wired to be social while others are hard wired to be loners. If the momma is worried about any delays or emotional issues then maybe a dr would be in order... But I also think that drs blow some things out of proportion and try to medicate for EVERYTHING...
It may sound odd, but we always "practice". Lets use going to church as an example. You can't expect young kids to sit still for any amount of time if they never have to. So we set aside a few minutes daily and the kids get books and have to sit on the sofa (quietly) and read their books.
So, your friend can turn it into a game. You sit here while I sit here. You play with your toys while I read the mail. When I'm done... We will play.start with just one letter, then thru the weeks try to lengthen the time.
(here is where some may want to turn your eyes 'cause this is where it will start to get contrevertial)...
What is YOUR reaction when she hits your child? Do you stand by and let the mom deal with it or do you step in and snatch that hand off your child and get down on eye level with her and tell her firmly NO! you do not hit. Time out for you! Some people may think that correcting other peoples children is a big nono, but you can not be in 6 places at once! If your child is doing something OBVIOUSLY wrong (like running for a major roadway) and you arn't easily accesible to stop them NOW wouldn't YOU want someone to step in and bring the offense to light (or physically stop them)? Maybe this child has never been confronted by someone outside of her comfort zone.
(note: when I say spanking in this next section I do not mean beating. There is no emotion involved in it. It is a thought out justified punishment.)
I personally do condone spanking with conditions. If my child would take off running purposely towards a major road that would for sure get them a swat. I only pull out the spanking card for INTENTIONAL and DANGEROUS behaviour.
It may sound bad. But as children you HAVE to train them. Training begins and ends with consistancy. If you say NOW... it means NOW and if they don't move that means YOU have to go move them to where you were when you said come here NOW!. (I never get to 3, If I call you and you arn't moving by one, I'm moving by 2...)She is testing her boundries on a continual basis. I do not know what boundries your friend has set up or how consistant she is with them. But that is the BEDROCK of behavior. Knowing your boundries and what the expectations are.
My kids know that they can play and have fun... But if momma sees something and calls you, YOU COME. If I have to get YOU, YOUR fun stops. Time outs or going home.
There are many things that are not told in this post. Does mom/ punisher get on the child eye level when speaking with her. DOes she maintain eye contact? Physical contact? Point? yell?
The reason for the eye contact is so YOU know they are paying attention. At first she may have to remind the child where to look. (I snap my fingers at MY eye level and say "Eyes" while kneeling down to their eye level.) EVERY time they look away. I do not speak unless I am staring into their engaged eyes. Also maintain physical contact. Not squeezing arms or anything. But kneel down and place a hand on top of their hands or on thier shoulder or even pull them into the crook of your arm, say your piece while maintaining eye contact then Hug them. (that makes sure your not Pointing accusitory at the child)