1.YOU DIDNT EAT
The constant reminder from your parents I don't believe you, you didn't have dinner you are lying.
When the truth is you had dinner and more and even if they believe you you can tell by heir look they are lying.
WHAT TO DO?
Honestly, nothing. You know the truth, you aren't lying to yourself and that is the most important. The truth is that they are still scared and confused and trying to figure out your situation.
The most important this is that you learn that you are worthy of telling the truth to yourself.
If you know you ate and didn't exercise or purge but your parents look in eyes and don't believe you. Swallow that and you will see the results. The results are your body getting healthier and healthier isn't that awesome.
2. THEY WILL UNDERSTAND
Like I said give them time because they are sick of you telling them I'm going in for real this time and then giving up the next day. Prove them wrong make them proud, make yourself proud.
3.DONT LIVE FOR OTHERS APPROVAL
You are your own boss and living being. You aren't put on this earth to please and make others comfortable while suffering. Be true to yourself and live for your expectations.
4.TALK
And if you feel alone thy to talk it out with them, if they don't listen write them a letter. Write my in DM, reach to psychiatric, write in your journal, and express your emotions.