I'm thinking about an idea, but I wanted to know if it is even possible. Can someone please let me know, and how?

My sim lives in Moonlight Falls, but I sent her to Bridgeport for vacation, while there she met and married her husband. This gave me an idea, but I'm not sure if it will work or not. I was thinking about keeping her and her family in Moonlight Falls but wanted to send them to live in Bridgeport in a vacation-type setting on a regular basis. Is this even possible to bring babies and toddlers on vacation with them? If it is, what are the settings?

Yes, but you have to unlock the option if you haven't already done so. On City Hall or an in-game computer, NRaas > Traveler > Allowable Travelers. The youngest one (I forget which ones show up on the menu and which ones don't) should unlock both babies and toddlers.