Don't give up helping your boys with learning how to use the toilet. Summer is the best time, because accidents aren't a cold nightmare to change. Some suggestions:
First, yes, ditch the pull-ups. They are nothing but glorified diapers and cause confusion. At bedtime, I'd suggest using a standard diaper, so they know the difference of what they are wearing. When they are in the habit of getting up from naps/bedtime dry and then using the toilet, that's the time to move into training pants (with your plastic covers over them) for bed.
Second, out and about, you have options. Take a small potty out with you to the park or other areas, visit the bathroom upon arriving at the mall/stores, and bring lots of changes of underpants and clothes, plastic bags to put the wet clothes in, etc. Kids get very distracted by play, and so accidents are common until the child decides being wet and having to be changed is more unpleasant than leaving the activity. Being wet and having to be changed is a great natural consequence, so you don't have to provide any incentives or punishments...just let them do this on their own.
When you are out, have the boys wear waterproof shoes/sandals, so if accidents occur, shoes can be washed off easily with a water bottle.
You sound like you are providing great support for your little guys. Kids have their own timetable on this sort of stuff, my son is right in the middle of this process. If your child isn't self-directed for getting to the toilet, be sure to provide invitations to using the toilet (don't ask 'if' they have to go; tell them "it's time to use the potty" and then gently help them away from what they are doing). Your boys are just fine on time, it sounds like you have really let them get to a reasonable point of maturity...now it's time for them to do their good work too!
Best blessings and plenty of patience!:) I'm right there with you!