No worries!

I rarely get to stay in Valencia the night before either.
I've just noticed that it doesn't say anywhere about how long it takes to get from Torrevieja to Alicante. As mentioned, traffic can be a killer. It shouldn't take longer than an hour. But I would say give it at least an hour and a half.

The other problem you're going to encounter is getting the tickets for the bus or train in time. Even if you pre-purchase a ticket for the train via internet - it's very possible that you are still going to have to get a numbered ticket and wait your turn at the Renfe station in Alicante. The 'localizador' doesn't always buy you time, it just buys you an actual seat. (And morning train tickets do sell out - it's not like Italy where you can stand or sit on the floor).

If you can, try and book all the tickets you can before the Monday. And allow yourself at least 20 minutes (with train tickets already purchased) to get from the bus station to the train station. It's extremely hard to do it within 15 minutes - I know! - but 30 minutes would be comfortable.