I've found the only way to be able to switch characters in free roam is to first use the Shield Station and select a character. Once I do that, I'm able to hold Y to select any other character I have unlocked. I'm not sure if that changes after we beat the game.
I've honestly never used a SHIELD station to switch to characters other than the two available. Just hold Y and it should come up with the list of characters, press A on those you need to buy and once bought, any time you press A on them, you'll become that character.
"If you don't like something, don't watch it again. Why whinge about it on a forum to a load of divs? Don't worry about it." - Karl Pilkington
Once you complete all 15 story levels, you'll then be able to change by holding down Y. Before that, you have to use a changing station, which seems to "break" the story line flow and you can use Y after doing that, until you hop into the next level. The only tricky part is getting the character selector to come up when you have a character like Hulk or Spiderman, where holding Y causes them to change from normal to superhero.