Since you state you're pretty frugal, I'm going to assume that means you usually don't stay on an on-site hotel room. If that is the case, I vote for an on-site hotel room which includes EP, especially due to it being the summer and the fact that you state you have a family. I do not know how many children you have, but staying at a resort with the bonus of EP really pays for itself, especially if you have more than one child, as unlimited EP (purchased via ticket) is $99 for both parks, for one park it's $89. So, even if you stay at a resort for $300-400 and you have a family of three, or four, it's as if you're paying for three unlimited EP and not the room itself. Which will be useful during June. Also, it's nice to be able to walk, take a bus, or get on the boat to get to the City Walk, or one of the theme parks.
However, if you plan on doing that anyway, tell yourself what are you normally the most frugal about? Is it souvenirs, food, drinks? Whatever it may be, do not think about the price. Let yourself, or others have that souvenir they're eyeing, or have that extra snack, or drink. Go to that restaurant your family always been curious about. Purchase a ticket to that experience you've always wanted to try, but didn't want to purchase an additional ticket for, whether it's Volcano Bay, or something else on the resort, or Orlando area.
Personally, to me I always like to stay on property, but when I have the moment to splurge and I do not stay on property, or don't have the ability to, I always do the things I want to do, or have the things I've wanted that I've always held back on.