You can only apply from the address where the child actually resides.
You have to provide proof of address, and if you own a property, that is the one which will be taken as your address for admissions, even if you are actually staying somewhere else (even when renting with a proper leade, let alone lodging with family).
Prosecution is quite unlikely. Being stripped of the school place is however very likely, because parents (whose DC's genuinely local best friend did not get a place) end to report apparent anomalous allocations to the LEA. If they deem the application fraudulent, then the place can be removed even after the DC has started at the school. At which point you will be allocated a place at the nearest school with a vacancy. Which could be very inconvenient.
If however the school near your DMum is undersubscribed, then you will get a place even from a long distance away. Are there any undersubscribed schools near her?
How many slots for preferences on your form? You could use the first for dream school even though it would take a miracle, second for storially undersubscibed school that's probably workable, and third for school you're near as dammit sure you'd get a place at even though there may be all sorts of problems because it's still likely to be preferable to a random allocationof whatever the nearest vacancy might be.