If your girl is 16 mths, baby must be pretty small yea?
New addition to the family?Probably cause she is jealous.
Also maybe cause daddy does not spend much time with her, he is like a stranger to her but she knows you are mummy and just like you are puzzled about her behaviour, she is puzzled why "stranger" is getting close to mummy.Probably doing this as protection.
Otherwise, mayb she is trying to get attention but at such a tender age, not being able to communicate, she uses this as a communication device.She probably trying to get attention but not knowing how much strength she is using.
In any case, try to get daddy to spend time with her more often.bring her to playground .Swing her around.Put her on shoulders...Anything for them to bond.
Mummy dont't forget to continue spending time with her too.But do get daddy involved oh yeah and baby too.Go slow.
And yes do let her know that beating is not right:S. And its :"pain pain"