Thank you Ed (Intheswamp). Very good points! 
You are correct, 2 homes. The one in NY would be way up on a roof of the house next door as it is the clearest from large trees that surround us. Not easy to maintain. Any links to bird spikes would be welcome. I would have to get someone up on a very high ladder to do this. Can't imagine more than once or twice a year. There just isn't another place to put this that wouldn't be seriously compromised by trees. Any thoughts on how often do these batteries need to be replaced? (Unfortunately AAA alkaline.) Maybe at least I can find some AAA lithium if they exist. The one in Mexico will be easy, with accessible flat roof.
I don't know what to tell you on the batteries or the spikes for Ambient stations as I'm only familiar with the Davis stations.
The vendor that you purchased the Ambient from should be able to help you in regards to bird spikes. Also, there has been some DIY here on the forum regarding the spikes. Envision thin metal or plastic "spikes" fastened to a belt that straps or fits around the rain bucket pointing upward. The idea is for the spikes to prevent birds from landing on the lip/edge of the rain bucket and crapping into it...lots of times seeds and stuff that they've eaten will stop the hole up. You don't want so many that it will interfere significantly with rain collection but you want enough to deter birds from landing. Indeed the most frequent maintenance is cleaning out the bucket...in my case, mostly bird poop (I don't have spikes).
Lithium will probably be your best bet. Does the ambient have a solar panel and a super capacitor that charges up? You'll have to talk with other Ambient owners for an answer to what type of battery life you can expect.
Best wishes,
Ed
