Dear God. Easy Peasy Archery is a ridiculous feat. I'm not sure my DM would allow me to use that feat. I'm already +35 to hit with 28 dex. With that feat I'd be...what +44 to hit. I'm not even anywhere NEAR optimized neither.
I already hit on a 2+ and with Weapon Supremacy I can take 10 on all attacks AND get a +5 to any attack after the first. Taking 10 and not even counting the +5 I get on any attack after the first is AC 54 on the first attack.
Sorry about that. As to the OP, I would personally rule that the 2 feats do NOT stack. I would say that if you wanted to allow both, it would work as follows: Insightful Strike uses int instead of dex to hit (this is absolutely fine. No problem here.) The other feat doubles your dex and if you wanted to allow that (I think it's broken imo), would simply replace your dex. You don't double your intelligence. You just get to choose intelligence bonus over your dex bonus. So if you HAD both feats you could choose to double your dex or simply just use your normal int bonus to hit.
So if you had 18 int and 14 dex, you'd have the same to hit. +2x2=+4 for the double dex feat. The insightful strike feat is your int bonus alone which is +4.
Nowhere does it say you can replace dex for int in the feat. It says double your dex. Use int INSTEAD of dex. So you're giving up the use of dex, even if it's doubled so you can use your intelligence.
Anyway, that's what I think. Seems like a lot of people don't agree with that reasoning though.