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Without knowing your specific protocol, it is common to use more than one purification method for a single protein. Given the broad similarities that all proteins and even most biomolecules share, it is impossible to completely purify a protein in a single step. The strategy therefore must be to purify via as many properties unique to the target protein as ...
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Short answer: Unlike the physical model you're describing above, the reality is that localisation of biomolecules in the cell isn't a passive process, instead molecules are actively concentrated where they're required to be by a variety of different mechanisms.
long answer: I think possible 'missing pieces' of this picture which may help you reconcile these ...
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It seems to me that you are becoming confused because you are thinking of DNA in the same way that one things about small molecules.
When molecules are enormous, however, they act more like a material than a simple molecule and have no single structure. A good starting place for learning how to think about DNA as a large molecule is to learn about polymer ...
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