What is the product after treating ethene successively with chlorine and water, sulfuric acid, and potassium hydroxide?
The first reaction is a hydrochlorination reaction:



The second reaction is an acid catalyzed ether synthesis. The the solution is full of other 2-chloroethanol, which is capable of acting as a nucleophile in an $\mathrm{S_N2}$ reaction to eject $\ce{H2O}$. This is reaction will have a much lower energy barrier than the dehydration you proposed, which requires the extraction of an aliphatic hydrogen. The ether synthesis mechanism can be seen here:



The final step is a series of two $\mathrm{E2}$ reactions (shown condensed here):

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