Our daughter was home schooled, and I don't suggest it except in a few situations. Elizabeth is very, very smart, however she has poor social skills and doesn't accept authority well. She didn't get along with her teachers, and the quality of her school friends was, shall I say, sub-standard. We moved to an area where the high schools were far inferior to her previous school, and just had to home school.
We have neighbors that home schooled their 5 Air Force kids, and they were a smart but very strange bunch of kids. Their mother has a Masters in Education from Harvard, and she was like a drill sergeant in their education. Very few mothers have such educational credentials, especially if the children are brilliant. One just graduated college with a 4.0 in electrical engineering.
Unless both of your children are extremely well adjusted and doing well in school, I wouldn't suggest you home schooling them. It sounds as if one of your kids needs structure of a community and a high quality school. I just hope you know exactly why your younger daughter's having so much trouble keeping up.
My niece just returned from the premier ADHD clinic in the U.S. to have her 12 year old son physically and mentally evaluated. He's been in the top elementary school in the region, but he's just not ready intellectually to move on to the top Junior/High School with his buddies. We know he'll never be a doctor or lawyer, but we just want him to have less anxiety and get a handle on life.
Home schooling parents are going to be positive about the experience. My wife and I saw a "different" group of parents at home school meetings, and few that had the education or knowledge to properly guide their children in a self-guided home school program.