Hi snorkle - I would go for out for school lessons, they willprobably be cheaper anyway - I charge £11 for half an hour for piano lessons. Re practice, the only way to do it is to have a regular time slot when she practices - good ones I think are before school, immediately getting home for school or straight after tea, as then you have a 'memory prop' - it is part of a routine, rather than 'I've got to get some practice done some time today...'
Ideally she should do 20-30 mins every day, and I always say to my pupils that it is much better to do a little every day (even if it's only 5 or 10 mins) rather than a mammoth hour long session at the weekend, as it seems to be the frequency of practicing that makes most difference.
It sounds like she does want to continue, but maybe she needs a bit more 'hands on' support - can you do her practice with her maybe? Having taught for nearly 10 years now, and watching my 5 year old begin violin, I'm very much of the opinion that if a parent can be involved in the practice it is very much more productive - I'm starting to say this to all the parents of my pupils now.
Sorry this is long!