So, we hired a sitter to come to our house this summer so that our kids could stay home, go to the park, ride their bikes, and have an active fun summer with lots of friends over. I was extremely clear about my expectations for the sitter - we would pay her minimum wage, do deductions, and she would look after the kids, plan activities (she wouldn't have to pay out of pocket for anything but I didn't want to have to deal with scheduling activities if we were paying her to be there), and to do some tidying and light housekeeping. Minimum wage here is $10 an hour. She is a 24 year old university student on summer break. I made it clear to her (PAINFULLY clear according to DH) that my DS can be a handful. Also, I made it clear to her that he and his sister fight. Both things were clearly going to be challenging for her but she said she was up to all of the challenges.
The first week was great and the kids seemed to like her. Second week less so. She got sick on Wednesday night and so she didn't come in on Thursday. She texted me on Thursday afternoon and said that even though she was still throwing up and she was told by a doctor that she had stomach flu, she wanted to come in on Friday because she "needed the money". I told her that she should stay home, but I would still pay her for 4 days (even though she only worked 2 that week - Monday was a holiday that we paid her for even though we didn't have to). I don't know if she wasn't happy with that solution, but she seemed to have an edge after that.
Every morning when I came down the stairs she was reclining on my couch with my daughter's blanket over her. Every. Single. Morning. I asked her if she was feeling well, and she said she was. I gave her lists of things I needed help with around the house (I wasn't planning on making her be Cinderella, but I am paying for her to look after the house and kids!) and also lists of possible things she could be doing with the kids. Find out after that she is making the kids do things that were inappropriate, like clean up after the (old, 14) dog and getting my daughter to change the TV channels for her while she is lying on the couch (sense a theme???). Also, she is texting me constantly throughout the day, basically tattling on DS if he got upset with her, or was teasing his sister. Um, that's what I am paying HER to do. To deal with that stuff!
DH got upset, and when he got home this afternoon he told her that we understand that the kids can be rude, and that they fight too much, and that we are working on their behaviour. However, we want her to engage them more and spend more time interacting with them in a positive way, and not just when they are in trouble. Also, that it was inappropriate to be lying on the couch during work hours, and that it was making me upset that she was doing it in the mornings.
Fast forward to tonight: email QUITTING with no notice, completely leaving us in the lurch. She blamed DS for quitting, and said that he was basically uncontrollable. I know just typing this out that if this is the kind of person that she is (I think she is a nice enough girl, just freakin' LAZY) that my kids are better off with someone else, but we have NO ONE ELSE. I have a huge set of meetings tomorrow and DH has no annual leave left.

Farmed the kids out with friends tomorrow, going to try to get ancient MIL to come in for two days and then I'll take Friday and next week off and try to get a camp or something together. I promised the kids that they wouldn't have to go to camp and could stay home....
Way to long a post, but I needed to vent and get some perspective.
OP, stick with my post. It really is constructive criticism, and not meant to make you feel bad, because I know you are disappointed right now.
What I bolded would have made me quit and I am a lot older than 24. If your DH was mad, I can imagine it was a very unexpected, demeaning experience for the sitter. It would have been better to schedule a meeting at a time when the kids would be elsewhere. Both parents should have sat her down and calmly explain what they were noticing and the changes that needed to be made. She should have been asked what the parents could do to help her get on track.
It sounds like this babysitter got overwhelmed. The first 2 weeks were probably a honeymoon period and once she saw what she would have to deal with every day, she was kind of done. I have friends who are also teachers who nanny for kids who are a handful. I would seriously rather work at
Walmart than to have to deal with out of control kids and fighting all day long.
This is what I think, OP. I think in the future, you need to find someone more experienced with children who have behavior problems. Even if your child does not have special needs, this type of person will be able to handle and correct bad behavior when it starts. I also think you need to lay out your expectations on paper for prospective sitters to look at. A sample schedule of a day would be good. Something like this:
8:00-8:30--Assist children with breakfast, supervise getting dressed, brushing teeth.
8:30-9:30--Children play outside while you wash breakfast dishes, sweep kitchen and wash one load of laundry; place in dryer.
9:30-12:00--Outing such as the park, pool, museum, etc.
12:00-12:30--Lunch
12:30-1:30--Quiet time for children in their rooms(reading, quiet play, resting). You should relax during this time.
1:30-2:30--Craft or board game time. You should be interacting with the children during this time, facilitating their getting along.
2:30-2:45--Healthy snack
2:45-3:45--TV time(list channels allowed). Clean up lunch dishes, tidy up living room, fold laundry and put a second load in if needed.
3:45-4:00--Writing time--children should write one page about the subject of their choice.
4:00-5:00--Free play outside with you.
I think you need to come up with a list of outings for the sitter to choose from. Playdates need to be discussed. Discipline needs to be discussed. Like someone else said, have the person sit for you before the job starts so you can see how they deal with problems. I also think paying a little more(since it is 2 kids) would get you better candidates.
I nanny part time after school for a 5 year old boy(I teach during the day). I am paid $16/hour at this time. They don't require me to do any housecleaning, but as the little boy has gotten more independent(reading on his own, playing trains), I have been unloading/loading the dishwasher, doing laundry and tidying up. They really appreciate it, and I see it as giving them more time with their child. This little boy is really well behaved and smart. They don't watch tv, so he is always engaged with something hands-on.