Questions on how to sew non stretchy material onto stretchy material.

I don't have pictures of what im trying to describe or ask. so please bear in mind with me 🙏
I'm also extremely new to sewing but been able to pick it up decently easily.

But I've been making a cosplay of Frisk, from undertale. I'm trying to sew stripes onto a sweater and the sweater that I'm using is made from more of a elastic and stretchy material. Compared to the stripes which isn't stretchy at all. I've made a few attempts to sew on the stripes but it always comes out ribboned.

Are there any tips I could get that would help keep it from ribboning, and also give me more room with the sewing machine I'm using.