I believe there's no magic age where kids are okay on their own or not...Some are responsible at 10 years old alone...some adults shouldn't be left alone...
You are a mom...a very good mom. I am sure you know your kids well and know their level of maturity...trust your gut...there are so many different opinions on what is "right" and I suspect right changes with every situation.
I do agree the sitter sounds incredibly expensive. Many schools and churches have summer programs that are quite reasonable and fun. Is there a neighbor who might be willing to keep an eye on the kids before camp? I also found, when my daughters' sitter had to take a summer off right after she had twins, that some of the moms' of my children's friends were teachers or bus drivers and had the summer off and they were more than willing to make a little spending money babysitting.
Hugs...you'll be fine...One step at a time, trusting yourself and your higher power.