Hi John
i don’t know about a second battery but I can tell you that I’ve had similar problems with my stop/start on my 2015 XE.
I had it back a few times - dealer checked it over and said they’d top up the battery?
Something to do with auto stop/start only working when battery level is above a certain amount ... think he said 80% or something.
mine hasn’t worked for the past year now I’d say but I don’t really bother with it so haven’t raised it again with the dealer
Joe