In a lot of novels that take place in the Georgian era. For example in the novels of Jane Austen. Children live with relatives. Was is common to send your children to family and what was the reason for it.
It wasn't exactly commonplace, but it wasn't as unusual as it would be today.
Jane Austen's own brother Edward was raised by an aunt and uncle. He was the third-born, following James and George, but effectively, he was the second son: George was sent to live with a cottager family in a nearby village from a young age. (We know that he was epileptic. I've seen some sources claim he was developmentally disabled, while others say that he was deaf and mute. In any case, it was sadly common for gentry children with disabilities to be sent away from home.) The Austens' father was a clergyman, and his parsonage was owned by a wealthy cousin, Thomas Knight^(1); Knight and his wife, who had no children, noticed Edward in his early teens and had him come to stay with them often. When he was sixteen they legally adopted him, and a little while later they sent him on a Grand Tour for about four years. When the Knights died, many years later, he took on their surname as well.
The Austens were not as poor as the Prices of Mansfield Park, but they did have fairly ordinary means and eight children to raise (or to pay someone else to raise). The passing down of estates to family, preferably to an eldest son, was a pressing concern to ensure that they remained intact^(2) - so it was important to the Knights to have an heir of their own. This also proved to be a blessing to the Austen family later in life, as Mr. Austen's death left his wife and daughters pretty much on their own with a very small income. A few years later, when Edward's wife died, he allowed them to live in a cottage on one of his estates, nearish the old parsonage where James Austen was now reigning clergyman.