Interactive website for kids

That's a big "it depends" question, I think you'd need to come up with some idea of size of content and what your vision is with the interactivity of the website. Could change the complexity a lot and hence the timeframe and cost. Taking the games totally in isolation if we're talking simple 2D games like that it's a lot easier and probably could have it done within a few thousand dollars. Maybe even less looking for people on elance/upwork or odesk. But would require some work upfront to get a better idea of design. I'd personally avoid Flash development as those games on that site are built with (bit of a dying technology to say the least as far as websites), try and find some good html5/javascript game developers or even Unity developers (all my contract work is web based Unity build applications/games so I know you can get much more sophisticated games if you wanted but that's budget dependent).

As for the website itself.... that's very open ended unless you pretty much want the content to be pretty much just the games. Even so if you wanted things like leaderboards and things that will add a whole layer of additional development. But overall if we're talking of a website essentially of just the 4 games with simple 2D ish Flash-like games as on that site I go back to probably a few thousand (can't really give a more definitive guess than that without planning and nailing down some of the game functionality and graphics needed).

I'm not sure what you're thinking in terms of budget but I want to put that in comparison if you think that's way out there, I previously made a relatively simple "6 scenario/game" 3D simulation with a robot that took me about 2 months development time, we were paid abut $40,000 and that was at a loss. One of our lowest paid projects. So you can see that it really can be open ended in terms of budget and how far you want to take it. So just keep that in mind and while ambition is good also make sure you don't keep expanding the scope of what you want (feature creep) because it will get out of hand otherwise.