The only way I can even make sense of this insane ending is to think that it would have fit the series much better years ago, and if we had never met and gotten to know the mother. There's a great review by Alan Sepinwall at Hitflix saying that the creators got invested in the chemistry between Robin and Ted years ago, committed themselves to this ending, and couldn't adjust when the series ran as long as it did.
Even if I didn't have a problem with the ending, the reaction of the kids rings so false to me. It's fine that they are encouraging Ted to move on, but the unfeeling and offhand way they talk about their own father having actually always been in love with someone else was ridiculous, and not at all "true to life" which is sometimes cited in defense of the mother's death.