Rainbow Cottageis a 1934 classic!
From the Grosset & Dunlap jacket flap:
Shyly, half defiantly she lifted the latch, opened the gate and stepped within. Such loveliness made her gasp. This must be heaven on earth! But to its owner, Grandmother Ainslee, it was just "Rainbow Cottage."
Sheila's story of her father's cruel treatment and desertion was hard to believe, so Grandmother Ainslee promised herself she'd make it up to the girl. That day was the dawning of a new life for Sheila.
But into this life came Jacqueline, the cousin who hated her...
Can't find an original hardback? Don't fret! You can get a vintage paperback copy of this classic. It's been put out by Living Books/Tyndale as #16 in the GLH series. You can often find copies online for $1.00 or so.