The GM can have his own desires about how he wants the situation to play out and still be fair in how he has it play out. It seems very plausible that a traumatized starving dog runs away from the players, that trying to have it take food from your hand won't work, and that approaching it would be viewed by it as a hostile act leaving it to respond in kind.
Traumatized starving dogs don't start friendly to anyone. Sounds like a misplaced expectation.
So no forcing here.
Seems to me like expecting a 12 to succeed in befriending the traumatized starving dog was a misplaced expectation.
Sounds like normal DM behavior of introducing new content.
Misplaced expectations. The dog should have been defensively hostile in that situation.
Depending upon the circumstances of saving the dog it may be an impact or not - since you didn't elaborate on how then this part cannot be judged.
Finally an example of forcing - profound unfairness (assuming dice fixing to that extent is frowned upon at that table - but under some tables even that wouldn't be viewed as unfair - and without that fundamental unfairness how can it be forcing?)
There is only 1 clear forcing move here. The rest of your case rests upon your description of the DM having a desire to keep a certain situation in play a little longer. But as previously noted - he can have that desire and still abjugate fairly.