After thinking it over, it’s not merely that one can have two motivations (which is also true), the point here is that the motivation is not the same thing as kavanah.
Even if the reason one undertakes to daven for another is selfish, they can still daven with kavanah purely for the other person.
Perhaps this is even the p’shat in not serving Hashem al m’nas l’kabel p’ras. Even if the motivation is for s’char, the kavanah at the time one does a mitzvah should be purely to do Hashem’s will.
If a girl undertakes to daven for another girl who needs a shidduch, she should completely put her own needs out of her mind, and just daven for the other.