Now, this is the step I don't quite understand on how we eliminate trust. Once Dina receives the 100,000 sats, what forbids her from denying to reveal R to Chan?
If she doesn't reveal it, Chan's 'payment' doesn't 'get through', as the channel state update script requires Dina to reveal R to receive the payment. Chan commits to the payment, under that condition and can't revoke this commitment either.
Commitment schemes in general, are a pretty great invention for this type of stuff!
Secondly, if Chan gets the secret R, what forbids him from not giving it to Bob (so he can later give it to Alice)?
Similar thing: Chan only
actually 'gets the payment' from Bob if he reveals R.
After that,
'turtles, all the way down'.

The 3 minutes of this video starting at 13:15 explain it quite well:
https://youtu.be/yKdK-7AtAMQ?t=796and now you all know that Dina gets paid using chens money
which if there is a break in the route. like if bob goes offline chen doesnt get paid
thus alice keeps her funds too because she to doesnt pay bob. and now Dina has been paid walking off pretty happy to get free money and alice walks off happy knowing dina accepted payment for goods designated to go to alice, without alice paying..
thanks chen you paid for alices goods
along with blackhat having issues of missing funds where he cant find the key to spend it via a simple methods.. and needing to hack his own wallet to find the keys(facepalm) are you guys now prepared to admit LN has flaws..
or are you all on the kumbaya bus of blissful ignorance