Since dimethyl ether is a weak Lewis base, you can experiment with adding various water soluble Lewis acids in order to create a Lewis acid-base complex and thereby reduce the volatility of dimethyl ether. What follows is speculation (no actual experience claimed). For example, some boron and maybe aluminum compounds may work (e.g. boric acid). Strong protic acids may help too, but they may cause at least partial hydrolysis.
You can't increase the solubility of DME in water. But you can convert DME to something else (like a Lewis acid base complex, see the previous answer), which is more soluble in water. However, this "something else" is no longer DME.
Actually there are many cases in which a weak Lewis acid-base interaction is enough to substantially change solubility while not enough to generate an identifiable compound. Addition of protic acids to water can probably do the job (provided that they are weak nucleophiles). However in a broader sense Yurii is correct: even if the DME is still DME, the medium would not really be water anymore...
The only ways to increase DME solubility without changing composition are to work at lower temperatures (where DME solubility is most likely higher), or if one has the equipment - at higher pressure.
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