Staffies can tend to play that way, body slams etc. I would say you suggested the right thing, to keep her on a long line. That way she can interupt the behaviour before it gets to the inappropriate level, and she can make sure she doesn't get the reward of getting to the other dog. I really wouldn't be telling her off, she is at a delicate age and the last thing she needs to learn is that when she goes near another dog she gets in touble from her person

I would interupt ask for another behaviour and then reward. I'll bet she likes a game of tuggy, so tell her mum to bring the tuggy toy out with her. She's going to need to work hard on becoming the most interesting thing to the pup when out and about.
Just getting her to meet as many dogs as possible, walking with them, classes, when I've got a pup to socialise I just bug people and ask if it's ok for them to say hello, usually with the aid of a long line.
It may also be useful if she can get people to go around to her home, I always like to get a dog to accept others in the home early on so it's the norm. Also that way, she could use a time out quite easily. As the pup is really keen to play with the other dogs, you could use that. Have her on a house line and every time she gets to rough, take the line and pop her behind a baby gate for 30 secs or a minute. That gives her time to settle a bit and she should start to associate the rough behaviour with the ending of the fun.
It would also be useful for her to meet with some adult dogs that are confident and capable of telling her when she has gone too far, without them getting scared or cross. She may still have a bit of puppy licenese at the moment but that won't last for long. She will get there, she's just being an over excited staffie puppy, the more she gets to interact with other dogs the less of a big deal it will become

Edited to add. It would also be a good idea to get her to do some self control exercises with the pup, starting with basics, like asking for a sit before she puts food down, asking for a wait at the door before she goes out. Teaching a strong leave with the aid of food and toys. Same with toys, tell her to ask for something before she gets the toy, if the pup gets over excited then the toy goes away. Ask the pup for a sit or down before she gets to say hello to other dogs, if she doesn't then she doesn't get to say hello.