Hello and welcome to COL!
I can understand you being concerned over Oscar's behaviour, you mention that you've had him two months and that he's one year old now, where is he from? Did the previous owner mention his problem?
It seems like Oscar is testing the water with your Mum, you could try this, make him sit and wait for everything he needs and wants, food (especially) walks, toys, etc. Groom him daily, get him used to being handled, don't let him on the furniture, make him stay at your feet.
What I did with my dogs to stop them growling over chew's was when they had one I would from day one approach them and stroke them and offer a small treat in return of them giving their chew and lots of praise, now there is no growling at all, I can take anything off them.
Please remember that 12 months is a difficult age, many dogs of this age push their owners and try it on with them, I'm sure there will be more experienced owners on COL that have had this problem will be more than willing to offer sound advice.
Good Luck
Lizzy Molly and Evie