what is your mother like?

长相。另一种:What does your mother look like?

what is your mother's character

你说的句子既可以问长相也可以问性格啊
硬要换的话 How's your mother looks like?

这是问长相，因为句中已经有了is这个动词，like不是动词，是像的意思
如果问性格的话，like就要作动词，应该是What does your mother like?