1) When it came to his sister, his mother gave her all she wanted. But she was extremely unkind to him.
Is '1' correct?
He had a sister. Their mother gave his sister all she wanted, but was extremely unkind to him.
There's no reason to separate 1 into two sentences, especially with the clunky "But" at the start of sentence 2.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.