The Leia/Han/Luke triangle was mostly used as comic relief in ESB. It wasn't credible, but there were a few good jokes and it felt a great deal more like sexual attraction rather than love. It still wasn't so well received at the time, and got somewhat evacuated from ROTJ.

The Padmé/Anakin story is built on a "tragic fairytale" mode and had to get to the "let's make babies" stage. The core element work - it's straight from mythology, but to put that sort of thing in a story and make it believable, you have to develop it, and the psychology behind it, far more extensively - and you can't do that in a SW movie and remain true to the style and spirit of the movies. The other alternative is to find the proper "mythological tone" (eg: Excalibur), but that's terribly hard in a movie that relies on "realism". So you have to take it at face value as a fairytale romance in a kid movie. Personally I didn't have a problem with it except with the silly uber-romantic Naboo scenes in ep 2 (though they were silly enough to keep me entertained by making me laugh).

What truly got in the way, IMO, is Padmé's character. Lucas never managed to make it credible that she would be at the same time so intelligent, mature and wise but would still fall in love with someone like Anakin, and give in to those feelings. I don't really blame Portman, she had to play a character that often didn't make much sense psychologically, and she had to work for Lucas. Lucas works like a European director, he's from the cinema/theatre school that let the actors do most of the work with the performances. They're responsible for "finding" and carrying the characters through the movie(s) - the director, who isn't an actor, interfere with the acting process as little as possible. The classic "American school" rather have the director far more involved in directing and shaping the performances with the actors during filming (and btw, the "schools" are referred to by their origin, nowadays many Europeans direct US-style, and fewer Americans but not only Lucas direct European-style). That explains in a large part how in the SW movies (directed by Lucas, vs. ESB/ROTJ with Kershner and Kasdan) the European actors deliver generally good performances and most American actors deliver performances under expectations (or very uneven through the movies, like Hamill and Fisher), especially those with little or no stage experience or formal acting training. Natalie Portman was usually quite good in the "political scenes" and in scenes with European actors (eg: facing Neeson or McDiarmid), but it's very obvious she didn't get the more personal/psychological aspects of Padmé (they didn't make much sense) and didn't quite know how to play her in those scenes, and Lucas was of little help to get her to find the right "B movie" tone for those. Christiansen had similar problems - he's rather good with other directors/characters. Actors like McGregor, Neeson, McDiarmid, the Swedish actress playing Anakin's mom etc. were all used to "European" style of directing/acting work, and pull it off far better. One just wonders why Lucas insists on casting Americans who rely on directorial guidance, when he can't direct them the way American actors are used to work in order to deliver good performances.

I think Lucas should perhaps have considered making Padmé closer to Anakin's age - that is, when he decided to make Anakin younger, he might have considered turning Padmé into the daughter of the Naboo ruler at the same time to keep her much closer to Anakin's age, and kill the ruler off - in the escape from Naboo for instance, to force Padmé to fill shoes too big for her. That she could have connected with an Anakin going through very similar experiences would have made a lot more sense, and the whole "juvenile love" much easier to swallow. Lucas idealized Padmé too much early on, and as a result didn't manage to give her a credible "fall from grace" into immaturity and bad judgement later on.

But considering these are movies for kids, the "and then bang! they're in love" aspect kind of works.