Mikki - if you boil a ham & all those vegetables for 3-4 hours, I don't know about the ham (there are several different types - not all of them suited to "boiling"), but one thing I can definitely tell you is that those vegetables are going to disintegrate into total mush.
When I make a traditional "New England Boiled Dinner" using a corned beef, the beef is placed in a pot & covered by several inches with water, water is brought to a boil & then reduced to a simmer, & the meat is simmered for 3-4 hours depending on its size. The vegetables (carrots, potatoes, turnips) aren't added until close to the end depending on how long each one takes to cook properly. That means potatoes & turnips go in around the last 20 minutes (depending on size), carrots next at 15 (again depending on size), & cabbage - in string-tied wedges - the final 10. (Although I really dislike boiled cabbage, so these days I prefer to thickly shred it & braise it in butter in a separate covered skillet.)