How to make my trains go through stations

I have a problematic train line that I had built originally for one to two trains, but now must support five, and I can't take it down and rebuild it for all five because of space constraints.

Originally I had a part of the main path contain a stop for my plastic factory. With trains stopping there for 60+ seconds created lots of clogged-up points. I added a small path around it so that trains could go around it when the station was full. This seemed to work at first, but then I realized that they would pile up at the split between the path with the train stop and the one without as unless the train was set to go to that stop, they would never go down the path with the stop.

Is there any way to make it so that the trains will see the path with the train stop as a viable path instead of just going around and ignoring it?

This is the way it's supposed to work. Trains choose the shortest path to a destination, but a path with a station on it gets a huge penalty. A path with a station on it would have to be enormously shorter for a train to choose it over a path with no station.

This is logical, because a train can get stopped for an indefinite amount of time at a station. A train could be waiting till it's full, but if no cargo arrives at that station, the train will never leave. So no other train wants to risk that.

So you'll probably have to either move the station you're going around, or move the station you're going to.

Factory redesign is a big part of Factorio. A good rule of thumb for starting out with enough space is that if you don't need a car to go between parts of your factory in a reasonable amount of time, you're probably not building it big enough.