I used the personal a - " a mis padres " - why is it wrong?
Your parents own this garden. "A mis padres" is not possessive; "de mis padres" is.
Is there a better way of writing "My parent's yard" than "El jardin de mis padres", perhaps using "su"? Like "Su jardin".
"Hay muchos árboles en ..." won´t work?
Probably not, since it's a different sentence.
"There are a lot of tree in my parent's yard."
"My parent's yard has a lot of trees."
Is césped not yard? Why jardín?
Cesped is "grass", not yard. Either jardin or patio is used to translate for the area around a house, where english says yard or garden