I saw it that we’d just had a story about the flower shop lady allegedly being けち, and that Spitz’s reflection was that he thought in comparison Fukuoka seemed more けち.
I don’t think there is much difference in your two translations? Something must happen, it’s the dog that has to do the remembering, and it’s being done for the benefit of Spitz.
By my limited understanding, 「おぼえてもらわなければならない」 tells us that the subject (“I”, by context) must receive おぼえる from a second party (marked by に).
Thus, I would say:
okay, that makes sense! thank you! 
Page 60:
おれは、花をえらぶふりをしながら、さりげなくアルプスを花屋のおくさんのそばに、おしやった。
“Shoving” the dog towards her sounds so… violent? But maybe the Japanese (or even the English) meaning doesn’t necessarily come with that negative connotation?
Page 61:
So he didn’t buy the flowers (and left the shop) because they are so expensive, right?
(I probably just have to read on and will know the answer…?)
I took it as pushing Alps in the right direction. Which would probably require a shove given his size! I don’t think it’s supposed to mean in a violent sense.
And for your second point, that’s what I thought too.
Buying the flowers for the girl would mean skipping dinner by the sound of it. Personally I think he made the wrong decision. Get the girl and he could eat well for the rest of his life…
I thought the dogs would skip dinner. Faced with a pack of hungry dogs, I’d probably go with his choice.
