More context is really required here. Lots of people in their responses are drawing parallels with their own experience without really knowing what is actually happening here. There are nuances which really matter
Generally in social situations, the thing to do is use the common language, or accommodate those whose language skills are weakest with the bilinguals helping the conversation along
This however is a home situation, so I would from an understanding of why you are sharing a home , as PP mentioned, are you 'caring for' your mother or is she providing a home for you?
If she is providing the home (esp if she is paying the bills) a bit more of her language would be forgiven.
If you are both caring for her then English anytime the English speaker is present would be reasonable.
More effort would be made at more formal situations, so when eating meals use the common language. However, when cooking, if there were the two of you together I would almost expect that you would be using at least the Italian words.
If the only-English speaking person has cooked then all cooking and eating and clearing up should be in English.
In my experience of growing up in an English speaking household in a multi lingual community, these things usually organise themselves naturally.
When they go wrong, the language mismatch is usually revealing something else that is broken about the relationships.
For example, the families expecting their grandchildren to speak their language.
Then, it's also worth considering that, once you get beyond social chit chat, very few people are completely language neutral. See PP about who tells her children off in their native language. There are some things you really want to talk to your mother about using the language that is familiar to you from childhood.
This is the main reason I would always encourage people to try to learn another language, so that they really get the overhead and frustration of using another language, at different levels of fluency.
I'm afraid I would find it difficult to listen to someone playing the 'we are in England now' card precisely because of the 'cringe'. There are plenty of English only speaking people around the world who have no intention of learning any other languages.
This might be reasonable as a tourist/customer but few people trying to sell or influence find that helpful.
As for learning, no one can teach anyone anything that they are not motivated to learn. How much more motivation does anyone need, than to be in a relationship with someone who has cultural links to another language. How can you understand that aspect of their partner?
So, OP, happy to provide an analysis once we gave the important background details.