"Beijing is in China."
The sentence indicates the location instead of the verb. Since Beijing and China are both locations, we want to locate Beijing in China. 在 is used here to specify that, so the sentence
literally means "Beijing in China". Note that 是在 is not included in the sentence.
The meaning of 里 would be "in/insidw" when something is being physically enclosed (say, within 4 walls and a ceiling, inside a bag/box/container). This concept does not extend to "in" geographically. So you can say 我睡在车库里 I sleep in the garage (because it has walls and a ceiling) but it is not good to say 我住在北京里, or 我住在中国里。Certainly this is just a simplified explanation and you may find counter-examples. Hope this will still be useful.
北京是在中国 is not complete grammatically.
We need a noun or noun equivalent on both side of 是, A 是 B.
So these are correct:
北京 是 城市。
北京 是 首都。
And these are not correct:
北京 是 很大。 XXX
北京 是 很美麗。 XXX
北京 是 在中國。 XXX
All these we need to use the structural particle 的 to make B a noun equivalent in order to have a grammatically correct sentence.
北京 是 很大的。
北京 是 很美麗的。
北京 是 在中國的。