My five month old wakes a couple of times in the night, but really only needs a feed once. Otherwise I try to settle him by returning the dummy, if that doesn't work, patting and shushing, if that doesn't work, a cuddle (sometimes I get a burp which settles him) and as a last resort, the boob. The latter works 99% of the time. We have a very rare occasion when he decides he is a wake and wants to play - I just refuse to engage, make no eye contact, don't talk apart from sh... sh... , keep things dark and keep shushing, keep offering the boob, and eventually he'll drop off again.

You ask if this is 'normal', so I'm giving you my story of a better sleeper, just to let you know what is 'normal' for me. I guess it's really common to have a bad sleeper, but I guess if I were you I'd keep trying things to improve her sleeping, in order to improve life for you and therefore all of you. You don't mention what kind of things you have tried, so it's hard to suggest anything else...