Hi,
My advice would be to pick one domain name and force it to that domain name.
See Forcing a Preferred Host Name.
It is bad for your SEO (Search Engine Optimization) to have the same site responding from more than one host name, it dilutes the ranking in search engines across the 2 host names, so there are good reasons to force a single host name and ten you will also not have any trouble with the google map.
Note also that the Bing Map does not require an api key so you could use that instead but really it would be best to force a preferred host name.
Hope it helps,
Joe