Thank you for your question! Hopefully I can help alleviate some of the frustration that you are feeling as a parent and teacher.
The first year of homeschooling is always the most difficult because you are learning the ways of homeschooling, and your children are learning how to be homeschooled. Therefore, it is understandable that your daughter wishes to work side-by-side with you for right now. This is very normal. Gradually, however, as she gains more confidence as a student, she will become less dependent on you and more independent in her learning. You might find that this will be true for your son, as well.
Helping your child become an independent learner is an important aspect of homeschooling. In the regular classroom, children learn to work on their own, simply because the teacher cannot spend that much time with each student. In homeschooling, it is easy for the learner to become dependent on the teacher, because the parents are always around and can provide that individual attention.
It is a good idea that you are using a reward system with her, to help her become an independent learner. At first you will need to think of various motivation techniques. You could perhaps set a timer, telling her that after two minutes of working alone, when the timer rings, you will work with her. You can gradually set the timer for a longer time.
Another way to help her become independent is encourage her to explore her world on her own. When you are teaching, you will discover topics that she might find particularly interesting. You can foster in her a desire for learning on her own. When she asks you questions, such as "Why?" or "How?", have her explore independently. You can look it up together at first, and then gradually encourage her to look it up on her own. The library is a good source for materials which she can read on her own.
Good luck and God bless you and your family!