Because you're best friends that means you two are so close that you can talk about everything and you both should already know your own parenting philosophy.
If you have a play date in public or at her home then you can't do as much but you have every right to say out loud to your own child, "I better not every catch you doing something like that!" and to remind her child that she is being inappropriate and tell her not to treat her mother that way. I wouldn't have a problem telling my friend not to allow her child to walk all over her and to discipline her or she'll have big problems later.
If they're in MY house I would have zero problem telling her child how to behave because I have house rules where I live. So I would tell the child to stop or whatever if I saw the mother not doing anything. And then tell my BFF that I already have kids to tend to and she needs to step up or we can't get our kids together cuz I can't have my kids picking up bad habits. I wouldn't bark at my friend but I'd discuss ideas and help her get some kind of order because I'm sure it's not laziness. She probably feels overwhelmed and doesn't know where to start, doesn't want to be the bad guy and so on. But I'd set an example for my own children as they come first and not allow such things to go on in my own house and not in front of my own children.
K. B
mom to 5 including triplets