"OK talking about 60D, I heard the 50D is just the same but a cheaper alternative? Is that true?"
No. The 60D has a newer sensor, it uses the same as the 7D, 600D and 550D. The 600D on the other hand really is basically just a 550D with flip out screen.
The 50D is still an excellent camera in terms of build quality and feature set, but the sensor is aging - this is especially visible in terms of its high ISO performance, which should be a relevant factor to you based on your stated requirements.
Frankly, i'd ignore any camera salesman that tells you any stuff about "this camera has better color depth". It's irrelevant information. All current DSLRs have very good sensors and you won't be able to exhaust their capabilities even with five to ten years of intense practice. Hence small differences in color depth just don't matter at all.
You seem to have one big misconception:
You understood correctly that fast shutter speeds are useful for freezing motion, but shutter speeds are not a property of the camera. It is not so that you could take two different cameras and then get a higher shutter speed with the one than with the other.
The shutter speed that you obtain depends on the amount of available light, the aperture setting of the lens and the ISO that you set the camera to. In practice shutter speeds of like 1/8000s are only obtained in bright sunlight with a relatively wide open aperture. A camera only going to 1/4000s is not a relevant disadvantage, and 1/500s already is sufficient to freeze the motion of playing children. 1/1000s is sufficient for pro sports.
In that sense the D7000 actually beats the 60D by the way, as it performs better at high ISO values. Higher ISO means faster shutter speed in not-so-bright situations, but also more image noise. The D7000 develops less image noise than the 60D, so one can use it at higher ISO.
Ignore weather seals. They are a moot point unless you also intend to invest into weather sealed professional grade lenses - without these the camera might resist water splashes, but the lens won't. Also even with a 7D or D300s i'd hesitate to actually put the seals to the test. They don't mean that the camera is water proof, but merely that it won't be killed by a few raindrops. Pros use rain covers even on their tough-as-tanks 1D or D3.
I wouldn't consider the stock lens of the 60D to be a big plus. It's decent as a long range zoom, but not particularly good and not suitable for playing children indoors either. For that you'll need a 30mm or 50mm prime lens. Much better image quality and a better maximum aperture so you can obtain the shutter speeds necessary to freeze their motion.