I want to go to my grandma's home.这是对的
此时的“home”作为一个名词
但是当go home 连用 则作为副词
所以不加其他词
而“I would like to get to my grandma's home on the bicycle.”
应改为“I would like to go to my grandma's home on the bicycle.”或
“I would like to get my grandma's home on the bicycle.”
因为get为及物动词