Expenses
As a nanny I have a tight weekly budget. I doubt my employer will mind me telling you it's £20 per week.
This is to cover ALL activities for 2 pre-school children - similar age to your own. We do quite a lot of activities one way or another - though not all of them cost money! I feel your new nanny needs to learn to budget better and to do activities which don't cost a fortune. For example, indoor play centres may be great for some people, I personally dislike them and can't afford them often - they are a treat. Walking/Running/Climbing in the countryside/park is just as good physical activity and it's free.
Your nanny should not need to be purchasing snacks/drinks while out. With planning she can take snacks/drinks from home. My two tend to have a bottle of water with them much of the time when we are out. Tend not to take snacks, as want them to eat their lunch, though on occasion may pack some nibbles such as fruit, rasins, rice cake, bread sticks, carrot sticks etc. We also do Picnic Lunches when weather is suitable.
Late in the morning
This is BAD if it's happening on a regular basis and needs to be dealt with. If it's just on a couple of occasions then maybe it's traffic related and new nanny needs to get to know route(s) better. When she is late, you need to find out why. Perhaps she has trouble waking up in the morning! Reliability as a nanny I feel is vital. Also, make sure you return at the time you say you will. Lead by example... I'm sure you are already.
Leaving quickly at end of the day...
If you pay up to a certain time, then nanny shouldn't really leave before that time, unless agreed with you.
If you want there to be a handover period, then discuss that with your nanny. Perhaps it may be good to have one evening per week where you get home a bit earlier/she stays a bit later, so you can have a chit-chat over coffee, while the children watch a dvd or something (trouble with handovers, upon a parents return, the children will tend to want their parents full attention).
As you have had a nanny before, try if you can not to compare new nanny with the old one too much, as every nanny will be different and it will take time for you to adjust. I'm sure there are things about the old nanny which you didn't like... though also things you loved - so try to mold the new nanny into the nice bits of old nanny. Not sure about considering old nanny back again - would depend a lot on reasons for why old nanny left in the first place!