You pose a very interesting question. On one hand your son has been attending Catholic school for several years and is doing well. You and your husband are good parents to choose that choice of education for your son. On the other you are considering homeschooling because of Catholic school tuition. Many catholic parents empathize with you, when considering cost of catholic education.
Pray for the remainder of the school year for God to guide you in your discernment, and don't make a decision overnight. Let's look at the benefits and hardships of both forms of education. Catholic education, through Catholic schools, can be wonderful. I, personally, taught at a Catholic school and found the school families to be beautiful examples of "domestic churches;" and the children to be, for the most part, well behaved and respectful. The true teachings of the Church were taught. Teachers coveted Catholic doctrine, scriptures, prayers, and sacraments, and passed this love for the Church to the children. This was a Catholic school to be praised.
However, if your son is attending a Catholic school that doesn't follow Catholic doctrine and teachings, he may not be getting the catholic education you want for him. For example, some Catholic schools may encourage individual Confession in the fifth or sixth grade, rather than before First Eucharist. Or, they may hire protestant teachers. They may teach children about topics that you and your husband would prefer postponing or teaching yourself.
You don't need to be concerned about socialization when homeschooling. Purchase or borrow a copy of Kimberly Hahn's Homeward Bound, a great start to reading about homeschooling and its benefits. Mrs. Hahn will explain the many avenues for socializing in homeschools: co-ops, church functions, sports, music, etc. Your family can meet many kind, loving families and supervise who your son knows at the same time. You mentioned that your son doesn't seem happy at his school. Is it because of the social situation at his school? If some of the children are behaving in ways that go against the way he is being taught at home, perhaps he is bothered. Or, maybe your son is learning some social skills that go against our faith and he doesn't feel good about his religion right now. Is someone being unkind to him every day when he attends school? Sometimes there are more reasons to be concerned about socialization in a school setting than there are at home.
Homeschooling is a beautiful educational choice. As primary educators of our children we choose when and what we want our children to learn. We have opportunities to teach our children about our rich and full faith. This faith can be lived through out each day in prayer, sacraments, daily Mass (once or more a week), history, science, social studies and language arts, just to name a few. You and your family will also have more opportunities to live your faith in family life through character building opportunities. Your son will be able to help you with his sister, a few chores around the house each day, or help Dad with a project. These opportunities arise more often when your son is home.
One on one teaching and learning is also a benefit of homeschooling. When my children struggle with a math skill we don't have to move forward with the "rest of the class." We can slow down and work on that skill for as long as it takes to master the skill. If we are interested in the missionaries that traveled across the early United States, we can choose to read about them for a month. Individual learning is not only a great way to learn, but it's lovely time shared together.
Do not worry about your three year old daughter. In fact, having her brother home with her will be a blessing if you choose to home educate. If you can find a friend who homeschools, write a list of questions and ask to spend a little time discussing the joys and difficulties that come with homeschooling.
Two final thoughts: if you choose to homeschool your son next year explore our curricula. Lesson plans to pace you through the year, and excellent, creative standardized books are at your fingertips. CHC curricula is amazing help for first time home educators. Secondly, don't throw in the towel halfway through the year. The first year will be difficult, but it gets easier, and you may find that you can't wait to start teaching your second child. Keep praying for guidance.
Blessings to you and yours,