There is only one reason that you might want to get back into Mothers Cradle after leaving that is to obtain the power core that is inside the mountain. When you go back the gates are locked and there is an invisible wall stopping you from getting back in. Some people say that you can walk back across the bridge and then back again and the doors open, but this didn’t work. I found a simple solution though. Here is how to get back into mothers cradle when the gates are locked.
Start by overriding a strider, there are a bunch of them nearby. Head back to the gates and turn to the right. Use the mount to make your way up the side of the hill past the invisible wall. Keep going until the mount wont let you go any further. Jump off and make your way to the top of the mountain by jumping over all of the rocks and hills. Be careful not to fall into the town, there is another invisible wall inside that will cause you to get stuck and need to fast travel out.
Once you get to the top of the mountain be super careful, or you will die like I did in the video. It worked for me the first time, so I know it works. Gently drop down to the ground through the gap in the beam. Have full health to be safe. Try make sure you roll out away from the wall instead of into it. Once you land, you can run into the mountain and go to obtain the power core.
For the full guide on obtaining all the power cores check out the Ancient Armory quest guide. Here is a video showing how to get to the mountain and obtain the power core in mothers cradle.