With good time management, you'd be able to take classes, volunteer, and shadow. Plenty of students do it when they're taking classes full time and I believe you'd have no problem doing it as well. Tutoring is an easy way to volunteer without having to do it for an entire day. When I tutored in college, I did maybe 4 hours a week MAXIMUM. With a thorough google search, you'd be able to find plenty non-profit organizations eager to take on tutor volunteers. Possibly even a local elementary or high school.
I'm sure taking 2 classes won't take up your schedule 5 days out of the week so shadowing once a week on a day when you have no classes would be a good option. If you did this from January to June for 5 hours a day (5hr x22 weeks) that would add an additional 110 hours of shadowing. Now I'm sure 22 weeks at one dental office might be a little heavy so I might switch it up between shadowing either two different dentists or one general dentist and one speciality.
You could get even more than that in for both shadowing and volunteer hours, but I think this is a completely realistic and manageable goal. As for traveling, I'd leave that for next summer.