Assuming you are talking about showing both at the same time, it doesn't appear to be possible. See
How to Make 2 MapView on One Activity
Updated to respond to comment.
Per the Google Map API MapActivity, "Only one MapActivity is supported per process. Multiple MapActivities running simultaneously are likely to interfere in unexpected and undesired ways." So even if you have two different MapActivities you have to deal with the Process Lifecycle, where perhaps one activity is visible and the other activity is background and that is where you are getting problems.
2nd Update
So according to this thread Limitations of the MapView and MapActivity one commenter put a separate activity between two MapActivities and was able to make it work, but otherwise you will have to use overlays/find a way to make your app work with only one MapActivity.