I coach my daughter's 10U softball team and I am throwing the girls an ice cream sundae party on Saturday morning after their game. I will have to leave my house around 7:30am on Saturday and the ice cream party will be around 11:00am, so the ice cream will be out of the freezer for 3.5 hours or so. This will be standard 1/2 gallon blocks of ice cream. Will regular ice be enough? Or do I need to make a trip to the store for some dry ice? And if dry ice, how much, and can I purchase the night before and leave it in the cooler overnight?

You will need dry ice, yes you can purchase it the night before, don't touch it with bare hands......probably 10 pounds for a medium-large cooler. DO NOT store it in your freezer at home.

If you use dry ice and regular ice together you will have the best results. Place the ice cream on bottom, cover with regular ice to fill the cooler. Place dry ice on top of the regular ice. Be sure to vent the cooler so that the expanding gases from the dry ice don't turn your cooler into a bomb.

Also make sure you use adequate ventilation. Carbon dioxide gas can be toxic. Read more about it here.

It's been a few years, but we transported a couple gallons of Blue Bell from Houston, TX to Bakersfield, CA in a foam cooler w/ dry ice.
Roughly 25 hours in the cooler & it was still frozen when we arrived, though the dry ice was gone.

There is such a thing as too much dry ice.

For a while we handled ice cream it was packed with dry ice in giant coolers. Some ass clown put a good 75#s of the stuff into the cooler with several hundred quarts of ice cream. IR thermometer read -40. That will seriously hurt you, the stuff sounded like ceramic tiles as we stacked it up.

Separate the product from the ice with a couple thicknesses of cardboard. One piece the size of a dictionary ought to keep 10 gallons cold for several hours.

If you can, get the cooler inside a drop freezer, first.

Also, your ice cream should spend a day or so in a chest freezer to get it cold - grocery stores do not, usually, keep their freezers as cold as they are supposed to.

If the ice cream isn't fully frozen, dry ice can cause some texture issues