I think the stitch you're trying to do is sometimes called the "trinity stitch", which makes sense since you're putting three into one!
I've made afghans that had panels with this stitch (I used Caron's Simply Soft) and it IS possible to make the stitch comfortably, even with thicker yarn.
The key to it is first, work the stitch below it loosely. If you do a tight stitch and then try to K-P-K into it you'll feel like you're breaking your fingers. I learned that one the hard way! I actually measured how far out I pulled the base stitch and it was as far as 3/8". When you do the trinity stitch it'll tighten up a bit so nothing will be all loose and loopy.
Next, I had to work out how best to manipulate the yarn to go from Knit to Purl and back to Knit in the same stitch. You'll have to play with this until you get your own comfort level established but here's what I did......
First, knit as usual but leave that base stitch on the needle throughout. Slip yarn forward to purl stlll leaving the base stitch on the needle. Then I took the right hand needle and lifted the yarn to the back so I could knit the third stitch and then took the base stitch off the left hand needle. By the way, I knit continental but it can be done comfortably no matter what knitting method you use if you just fiddle with it and work out the right flow. Then I'd give the little bobble a bit of a tug as I moved onto the next stitch.
It makes a really pretty bobble, more delicate than most, not too heavy. A sweatshirt with this sounds pretty cool.
Good luck with your project and let us see what you come up with.
Happy Knitting ,