But why would they go check on "the people at Hogwarts"? These are their children's teachers you're talking about. How many parents just pop in to the schools their children attend, just to check in? Harry and co trust the Hogwarts staff to do their jobs and look after their children. Sure, they have friends who work at Hogwarts (like Neville) but if they wanted to meet up with them, I imagine they'd be more likely to meet in Hogsmeade for a drink than randomly drop in on Neville's place of work.
I think Harry and co would understand how important it is that their children are able to use their time at Hogwarts to find themselves, develop relationships with people their own age and to grow independent. Harry constantly dropping in wouldn't exactly allow his kids freedom to do that.
The reason they're probably extremely emotional about seeing their children off is because they're going from seeing their children every day to months of no face-to-face contact at all. The kids may well come home for Christmas. It's just that going even a week without seeing their children isn't exactly easy for parents, especially if that kind of separation is happening for the first time in that child's life. Also, Ron didn't always go home for the holidays. I imagine Harry and co would very much leave it up to the kids whether they chose to stay at Hogwarts for the holidays - after all, they had some pretty amazing adventures during that time when they were at Hogwarts over Christmas.
Also, in the books Harry was studying to be an Auror (like a magical law enforcement officer, I suppose is the best way to describe it) so he certainly had every intention of continuing to live in the magical community.
I'm not sure where you got a Dursley vibe from Harry's behaviour at the station, to be honest. Do you mean a Muggle vibe? Because the Weasley family, the people you note are "in" the magical world day-to-day, aren't exactly prancing around Kings Cross pulling flowers out of their hats when we first see them. The only reason Harry figures out they're wizards is the owl cage and them discussing Hogwarts. And Harry's family in the epilogue has an owl ferret cage and are discussing Hogwarts.
Re: OP
I think Harry and co would understand how important it is that their children are able to use their time at Hogwarts to find themselves, develop relationships with people their own age and to grow independent. Harry constantly dropping in wouldn't exactly allow his kids freedom to do that.
The reason they're probably extremely emotional about seeing their children off is because they're going from seeing their children every day to months of no face-to-face contact at all. The kids may well come home for Christmas. It's just that going even a week without seeing their children isn't exactly easy for parents, especially if that kind of separation is happening for the first time in that child's life. Also, Ron didn't always go home for the holidays. I imagine Harry and co would very much leave it up to the kids whether they chose to stay at Hogwarts for the holidays - after all, they had some pretty amazing adventures during that time when they were at Hogwarts over Christmas.
Also, in the books Harry was studying to be an Auror (like a magical law enforcement officer, I suppose is the best way to describe it) so he certainly had every intention of continuing to live in the magical community.
I'm not sure where you got a Dursley vibe from Harry's behaviour at the station, to be honest. Do you mean a Muggle vibe? Because the Weasley family, the people you note are "in" the magical world day-to-day, aren't exactly prancing around Kings Cross pulling flowers out of their hats when we first see them. The only reason Harry figures out they're wizards is the owl cage and them discussing Hogwarts. And Harry's family in the epilogue has an
owlferret cage and are discussing Hogwarts.