visa status change

I entered Japan on a temporary visitor visa/status, then applied for a FT teaching job at a big company so I would be able to get a specialist visa. I was accepted, went to the Immigration, now I'm waiting for the post card from Immigration so I can pick up my residence card which should be due in a week. After an intensive course at the language school I realized that I don't want to follow their extremely complicated and controlling teaching system; at the same time another school I applied at contacted me for a part time job which looks much better. This school requires me to have a visa.
My question is: If I tell the language institute which filed the paperwork for me to get a visa that I am not interested in their job anymore, can they cancel my visa? Would the visa be valid if I don't sign a contract with the company who arranged it? Would there a problem with the school which is offering me a part time job?
I know the whole situation doesn't look kosher, it's not my style, really, but I didn't know things would turn out this way.

If you go tell the first school who sponsored your visa that you are not working for them, they are obligated to inform the immigration authorities within two weeks of that fact, and so are you. This in turn means you will need to get the second school to sponsor you for your visa (or resident status, if you are already in Japan).

Don't be miserable working a job you don't like.

Ok, the first one didn't work out - you need/should to tell them before you start. You could wait until the work visa is issued as the new job is same work area. Either way it looks like there will be an additional delay before you start working in either.

Technically, if you wait until the change of status is granted before informing the school and immigration that you are no longer interested in working with them, you will have committed fraud, since you will have misrepresented your intentions.

In any country, lying to immigration officials, even by omission, is never a good idea.

A technicality - maybe. The intention is to work in Japan teaching English - the degree or level of technicality is difficult to determine as once a visa (resident status) is granted they can change jobs without reapplying for a new visa. Also, as it stands the OP doesn't actually have a job yet, one (or more) offers because legally they are not allowed to work until the grant of residence - also depends what they have signed.

As you say, technical issues - whether they actually count or not - I do not have a telescope into immigration.

No; the intention is to do a specific job, involving specific tasks, for a specific employer, as stated on the application form.

I see that the OP has not yet signed the contract and the application to change to work resident status is underway - he has not eve started. Then if OP informs the first school of his intention right away, the school informs Immigration and withdraws the application, and that's it. If the second one is only offering a part-time position and requires that the OP holds a visa already (independently of them), that means the OP would have to look around again for another school to sponsor him for the visa.

It would be a fraud if OP waited till he got the resident status and then informs the first school of his intention; even after that, the school will inform immigration that you left, you also need to inform immigration within two weeks that you left, and considering that you haven't even started yet, the visa is likely to get canceled (though this is up to the immigration authorities; the school cannot cancel it).

Now this is not a legal point, but you don't want to start off your work in Japan with a fraud, neither would you want to start off with a school you don't like. I would suggest looking for a nicer employer from scratch.