From my experience with DS, it was a bit of a battle of wills for the first couple of months! He thought that if he made enough fuss I would let him give up but I stood firm and after a while he accepted that he would go to the tutor once a week and do the homework he was set. I tried to be consistent as to how much work he was set and when he had to do it each week. He liked to be given 20 - 30 minutes warning when he was expected to do some work rather than being told to get on with it right away. Also, apart from the summer holiday before his first 11+ exam, he didn't go during the holidays but still did a bit of homework. We usually worked this out by negotiation.
The tutor also helped as DS likes to draw and so does she, so at the end of each lesson she would let him do some drawings and she would offer advice. She also had some drawing books that she lent him - it all went to keeping his interest.
Try setting a timetable so you DD knows exactly when she has to do her work and offer some sort of reward programme (there's a thread with some good suggestions under Anything Else, I think).
Finally, as SVE suggests, if your DD thinks your heart isn't in it why should her's be? Try reminding yourself why exactly you're doing this (whatever your reason may be). For me, it wasn't all about the 11+ (that was an added bonus) DS was coasting along in a very disruptive class and I wanted to make sure that if he went to our local comp (which is pretty good) he would hopefully get into most of the top sets and be with other kids that want to get on and learn rather being continually disupted. As it was, he surpassed all our expectations and got a guaranteed place at GS. He has also learnt some new skills over the past year, with his English improving dramatically and it has boosted his confidence greatly.
Hope this helps - good luck with DD. I have to confess, I'm not looking forward to going through all this again with my DD - she is a lot more headstrong and stubborn than her brother.....