Sorry to see you here, @saffygirl - but you are in the right spot for support and info from those who've gone before you.
Your medical team will definitely be making decisions that they believe will give you not only the best visual outcome, but also hopefully, no recurrence in the future (tho sadly, this can never be guaranteed.)
Definitely chat with your breast care nurse about it - they often explain things in 'simpler English' than the surgeon.
The aggressive cancers can be the 'really sneaky ones' - that don't always present as a lump/tumour .... but can also have 'legs' that spread out & infiltrate other areas. Grade 3 is on the 'not so nice' end of results, hence them suggesting the mastectomy/2nd surgery and/or chemo as well as radiation.
Getting the 'clear margins' (as mentioned by @iserbrown) is what the surgeon is trying to achieve - having 'clean flesh' around the removed tumour site, as it is a better insurance against recurrence. If you think of it like a tomato - if there is a 'BIG off bit' - depending on the size, you'd throw out the whole tomato - as most of the tomato would not be edible. If it was only a small spot - you'd cut it out & eat the rest of the tomato - but if you haven't cut enough out - you will still taste the remains of the 'off bit' .... which shows you didn't cut enough off .... In a way, your Boob is the same. Quite a few of our members have had to go back for a 2nd surgery to get clearer margins - for peace of mind.
Maybe tomorrow, call the helpline here & have a chat with them? (The phone number is in the blue line at the top of the page.) They may be able to explain it better than us.
Whereabouts are you? If you add your town/city to your Profile, members in the area may be able to point you to specific services available to you.
As well as taking a buddy with you to your appointments, consider taping the appts on your phone too, so that you can go over it again later, for clarification. It is easy to miss bits, as it is all a tad stressful.
Ultimately, it is your decision & you have to be happy with what you go with. xx
take care & all the best xx