When dealing with other peoples' children, I tend to handle it like I would handle troublesome in-laws...very carefully! *grin*
The physical stuff (hair pulling, pushing) can be handled by removing your children and telling your friend that it is "apparent that nap-time is near" and leave it open-ended that way. If asked what you mean, you can just say that YOUR children get grumpy close to THEIR nap time as well, and that it's usually best to just leave kids to their naps. If you do this every time the kid does it, even if it's early in the morning, your friend WILL catch on.
As far as spitting, I'd say to her that her kid must have something bad in his mouth as you're *SURE* that HER child would NEVER do anything like spit at another child, as it spreads germs and the like. Be all "knowing" when you say it as well, but give her the opportunity to handle the problem while saving face.
And for cursing and screaming, I'd handle screaming like the hitting - like he's getting close to his nap, but I'd handle cursing far less tactfully - I'd say to my friend that I'm sorry, but that my children can't be around the cursing, and that I'd appreciate any help she could give me in keeping my children from picking up such crass habits.
HOWEVER, all bets are off if they're at YOUR house - you can tell your friend any excuse (I'd use "another friend" or a "business partner" of my husband's or whatever), but say that as you've had problems with that kid, that you've had to institute a new rule at your house (your husband and you agreed or whatever), and that they either have to leave if they become troublesome, or they have to spend some time in the same type of punishment as YOUR kids would (time out or whatever, but not spanking if you do that, of course). You can also reasonably say to the kid "I'm sorry, but we don't do <fill in the blank> at OUR house".
These are all answers I'd give in-laws, and believe me, I want to keep my in-laws, so I'm not giving you anything unreasonable. Just remember to try to stay as respectful as possible, and if need be, give "examples" of things you've had to do for similar problems - it could be that she's just embarrassed that she's having trouble handling the problem.