Stand your ground
Say they can join you for coffee if you really must but reiterate that you booked lunch for x number of people and risk her taking the huff.
I thought you might be talking about something like this.
I held DH’s wake at the village pub, it was a Monday late morning and while they couldn’t close altogether on our behalf they were confident that we would have the place to ourselves. There were so many people there, some I had not seen for years so when I saw a couple at a table that I did not recognise I went up to them , welcomed them, thanked them for coming then discreetly tried to find out how they knew DH.” Oh we had just come in for a drink” they said! I smiled and retreated to my next brandy.
Honestly if you were in a pub and a load of people in black all came in together, wouldn’t you make yourself scarce? Not them, they stayed and D2’s MIL (who had early onset Alzheimer’s) chatted away to them as she didn’t know who anybody was anyway!