Two power sources, common ground and noise
No problem on both counts. But:

a) You'll get more answers if you draw schematics that are easier to review by following common conventions: Rules and guidelines for drawing good schematics ... notably, general flow of action from left to right.

b) The noisy VS could well affect the INA219. So if the measurements are worth taking, it would be worth fixing that so that it's protected from going outside the allowed Vs range and it's reasonably smooth... this should only take a capacitor or two, perhaps a regulator, depending on the problem.

c) If by "noisy power source" you actually mean a power source with a noisy ground, then you may have more to think about, both with respect to contributing noise to whatever's downstream from the TWL6030, and also to the computer connected to the I2C interface (which will also share a ground with this apparatus).

Hope that helps.