Opening your windows in the heat is the problem. Insulation isn't designed for heat or cooling. It keeps what is inside inside, be it hot or cold. If you want to keep cool air inside, don't open windows and let the hot air in and the cool air out.
Not sure on your night temps, but opening windows and doors overnight and letting the cooler night air in and then shutting everything before the heat rises outside helps keep the house cool during the day.
I'm in a hot, humid Australian city. It is awful over summer. Some days you open the front door and it just hits you in the face and sucks the air out of you. We get months of steaming heat. Up to about 32, not opening windows and doors during the day and using ceiling fans is pleasant. My place has good insulation and is typically 10 degrees cooler in summer, or warmer in winter, than outside. Over 32, split system air conditioning is great. I only use it from about 11am and turn off over night to sleep with a ceiling fan on low-mid. Initially I used the air con sparingly, until one particularly hot summer. Then I used at will. It was a $50 difference in electricity for the quarter, so I use at will these days. Again though, keeping the cold in is important, so only open doors and windows if outside cools down to mid 20s and there's a good breeze.
I've got west facing huge glass doors. Stupid idea, boils in summer. I've put up an exterior shade blind, interior heavy block out curtains and have tall plants blocking the sun before it hits the blind. I put a thermometer out there one day and it maxed out at 50 degress, so it gets hot with the full western sun and my living area would be oppressively hot if I didn't have the barriers.
Think about your winters and how you would keep heat in. Do you open windows etc or keep them closed? The same goes for hot days on summer. Insulation will keep the cold in as long as you stop the sun shining in and heating the air up.