No, your app is fine. 'How much money does my coat worth?' is incorrect, but 'How much money is my coat worth?' is correct.
Worth is a property of the coat, you see, so you need to use 'is', in a similar way to 'how big is my coat?'
You can just say 'How much is my coat?' and let the listener assume that you're talking about monetary worth.
If you were asking how much the coat does something, then you would use the word 'does'. For example:
'How much does my coat smell?'
'How much does my coat cost?'