So sorry about your Mum's diagnosis @LinSkin. is she healthy & fit (relative to her age) other than the BC diagnosis (which is obviously a big shock to her & the family.). Is she on many medications? Is she fully mobile?
You are wise to query the surgery/treatment ..... as you say, just the anaesthetic may take a toll on her - and it is great that she is still agile in her mind and you don't want her to lose that!
It is a tricky one. Grade 1 (even tho invasive) should mean the lesion is very small ... but only surgery would confirm that - and the other breast is still 'undecided', so unknown.
It is a decision that only you and the family can make in discussion with your Mum and her surgical team - they will definitely take your Mum's age & prognosis into account, to 'cause no damage' - which is most Surgeon's 'mantra'.
Ask the surgeon what they would advise if it was THEIR OWN 88 year old mother. Also ask how fast growing the tumour is likely to be and if non intervention is likely to shorten her life.
A friend's mother had surgery last year (aged in her early 80s) and is now on Hormone tablets but she is finding it quite tough. Personally, I'd be leaning towards 'minimal' intervention, to be totally honest. Hopefully she can enjoy her final years in relative peace, surrounded by her caring family.
Take care & all the best with your decision making xx