I’ve caught a lot of trout using a kids Mickey Mouse rod. While a short kids rod has some limits, I’ve used them in high country lakes and streams quite a bit. I often take one with me, and a small selection of spinners in a small hard case, when I’m big game hunting.

A more standard takedown rod in a hard case may suit your needs better. You can get them in a pretty small tube.

A 4 piece fly rod breaks down awfully small as well. The Sportsman’s warehouse fly rod I have often gets stowed behind the seat in my vehicle if I think there’s a chance I’ll get to stop and roll out a fly.

Bass pro offers free fly fishing classes. They schedule them when they have interest, so if you call and ask they might suddenly have one coming up. Sheels might as well.