Make the marinade by whisking the brown sugar, honey, lime juice, lemon juice, maraschino cherry juice, garlic powder, ginger, black pepper, cayenne pepper, pineapple juice, wine, hot pepper sauce, and soy sauce together in a large, non-metallic bowl. Toss the mushrooms, onion, bell pepper, tomatoes, and chicken in the marinade; cover and refrigerate at least 1 hour.
Preheat an outdoor grill for medium heat and lightly oil the grate.
On each skewer, thread a piece of chicken, then three of the veggies followed by another piece of chicken then a pineapple slice and one maraschino cherry at the end. Mix and match the vegetables as you assemble the skewers. Cook on the preheated grill until the chicken is no longer pink in the center and the vegetables are tender, about 10 minutes.