Are you sure that you are still in the period where you are given your full housing allowance?
Many companies offer a housing allowance at 'X' for 2 (or 3) years based on family needs, then the percentage the company pays declines in the 3rd, 4th and 5th years. And after 5 years, one must switch to a local contract.
This is because an expat contract is by definition temporary - there is an incentive to finish the project and move on - or to localize.
Anyway, just something to check out.
If that's not the case, and if you are
only staying because your employer needs you (and not because you want to be here), then play hardball.
Try to negotiate a more favorable housing allowance, based on your family needs and *your* research into housing prices - that is, real prices on Homegate, and the difficulty you've encountered in being considered for such places. Remind your employer that as a foreigner you are at a disadvantage in the local housing market, you are seen as an undesireable tenant and so usually have to pay up to find something suitable. And remind your employer that your definition of suitable might not be the same as the Swiss norm. (Which is why they gave you an expat housing allowance in the first place.)
Of course, playing hardball means that you need to be prepared to be told that your services are no longer required. Make sure you can live with that alternative before you head down that road.
Good luck.