In my opinion, diethanolamine wouldn't work that good. The mechanism is based on the fact that the ethanolamine is present in excess over your quaternary amine, and thus the "extra" alkyl group is preferably transferred to the amine function of the ethanolamine. Diethanolamine already has two substituents, and will probably not work as efficiently (it is also more sterically hindered to perform the reaction).
Note: It is always the shortest alkyl group that is transferred, so if you had butylpropyletylmetylammonium chloride, only the methyl group would be transferred from the quaternary salt to ethanolamine, giving ethanolmethylamine (HO-CH2-CH2-NH-CH3) and butylpropyletylamine.
http://rhodium.lycaeum.org (http://rhodium.lycaeum.org)