The image they have painted of the Hulk in the MCU is a very reactive creature of low intellect.
In Avengers, Hulk was able to stand his ground with the Avengers and take limited direction from Captain America. If however, the Hulk is provoked he becomes wild and uncontrollable.
Similarly, in Age of Ultron,
Banner is able to unleash the Hulk during a 'Code Green'. But in contrast is set-off and becomes enraged before the fight with the Hulkbuster.
While anger is what makes the Hulk strong, its isn't the only part of his persona. During the parts you are talking about:
Natasha approaches the Hulk with her hands up and speaks in a soft tone, because the Hulk is very much like a wild uncontrollable animal and says a phrase and touches the Hulk in a very specific way.
This seems to imply the Hulk isn't controlled by 'love' but by a very rehearsed hypnotic suggestion.
In addendum, its worth looking at why its Natasha who is doing the hypnotic suggestion and none of the others.
- Tony Stark - is afraid of the Hulk even in his armor, and is too brash and reactive himself, so I doubt he'll go up unarmed to calm the Hulk
- Hawkeye - is very self focused and likes to keep a distance as Selvig pointed out in the introduction of The Avengers, not only that he also:
has a family to worry about, unlike Natasha
- Thor - unlikely, as Hulk and Thor have come to blows on many occasions, so the would-be-king of Asgard would probably not calm him down
- Captain America - maybe the Cap could do it, he is calm under pressure, although unlike Natasha he's very much a pugilist and probably doesn't have Natashas expertise in psychology.
So, the logical choice is Natasha - she's smart, calm under pressure and the only one brave enough to face the Hulk. Keep in mind in her opening scene in the Avengers she was chained to a chair and dangling over a hole, completely unafraid. Plus, shes 'fought' the Hulk, and knows what to look for in a spate of rage and what might set Banner off. If there was an element of psychological control at play, Nat is probably the only Avenger qualified to control the Hulk.
Lastly, I think you have your premise back to front:
Natasha isn't able to control the Hulk because Banner loves her, considering how much Banner despises the Hulk (and vice-versa), Banner loves Nat because she can control the Hulk. The most likely back story is that given Natashas history of spycraft and psychological warfare, she suggested a hypnotic trigger to Banner, and that brought them together, not the other way around.