Brighton is definitely much more entertaining than Dover. It's a bit trendier than the typical beach community - very much London-on-Sea.
However I suspect that reading between the lines, when someone says they want to see the English Channel they mean white cliffs rather than a bit of sea that could be anywhere.
You need gently to probe what your sister means, otherwise you face a very rushed half day to look at sea only to disappoint her!
Either way, half a day is really tight. It's an hour on the train to Brighton, a swift 15 minute walk or short taxi ride to the sea, a bite to eat then back again, but - you know - the sea looks like any other bit of sea.
OR you do a full day and go & look at some white cliffs and maybe a castle or some countryside or explore all that Brighton has to offer.
Or you take your sister down to the Thames and tell her it's the English Channel and, no, honestly that really is France over there and not south London...