Actually, you're not as near the Marina (Marina Vallarta) as you are near the Maritime Terminal, where the cruise ships come in and from where a number of tours depart.
How old are the kids? Can they walk on their own? The reason I ask that is if they are very young and you have to carry a couple of them, it's a longer walk.
The only safety concern you will have from there, walking to an authentic market (called Palmar de Aramara) is heavy traffic so you would have to hold their hands over that very busy road. You'd walk down the road from your resort --- to the main highway. Then you have to cross the main highway (going toward the direction of Sam's Club and the Deck 12 condo complex --- which you can probably see once you get to the main highway).
Once you get on Prisciliano Sanchez right south of Sam's Club, you walk inland --- away from the water --- for awhile and find the market. It's large but it is authentic, as you mentioned. An established large neighborhood market.
Here is a map which might help.
It's the only authentic market (of any size) within walking distance from you. There are others that you could bus to. If you buy a lot, you could always take a cab home. Same zone = 40 pesos.
PS to edit: looks like I gave you the map right above where you are so just go down to the bottom and click the blue link which says to move down. Both your resort and the market are labeled. Have fun.
Edited: 4:40 am, November 23, 2012