So if you went to another flight school, did a rental checkout etc, then rented their airplane, it wouldn't be classed as flight training towards a certificate and should be allowed regardless of whether you have an M-1 visa or not. So yes, you can rent elsewhere as a private pilot (with instrument) and just be subject to that flightschool's rental requirements.
Uh..not so fast..slow down a moment.
If you are enrolled in a
course of training such as a Commercial training course then the time building may very well be part of this training towards a certificate or rating.
Something you will need to discuss with the school in question and whether they will allow it or not.
Some schools have been quick with canceling visas.