"Does she play with my daughter?"
Translation:Spielt sie mit meiner Tochter?
Little trick I learned in Latin, Tochter ends in er meiner ends in er. Alot of the times the ending will match up. Its not foolproof, but there are patterns for weekend warriors like us its about the best I can do. Or, man up and go hardcore by memories every gender for every word, every case, every chart, ect... When they started mixing two different cases with with 3 different sets of word ends in one sentence. LOL, I gave up weeks ago. Good luck.
I read that meiner is not Accusative, it is genitive wich is in next lessons http://www.canoo.net/inflection/mein:Pron:Poss:1st:SG
Dative part of the sentence is "mit meiner Tochter." First part of the sentence (Spielt sie) is in Nominative case. Imagine if that the sentence would be: She is playing with HER daughter. Preposition "with" indicates change of case and when you are asking WITH/TO WHAT you use dative after the preposition. In my expample you use both She/Her in one sentence and its still right. In german it would be: Sie spielt mit IHR Tochter.
Hope that helps a bit. I am just learner like you but thats how I understood it :)