ExMil how do I handle this?

[fortygin]

Quick background:
Was with stbexh for 24 years (since age 15), married for 14 years and separated for a year.
Have four DC 13, 12, 10 and 7.
Stbexh cheated multiple times over last 6 years and when I got photographic evidence and a letter from last OW we separated for good.
Ex is quite closed off do I have been sending any photos I take or funny thing dc do to exmil.
Co-parenting with ex has been up and down especially since I met someone else and ex accused me of 'splitting up the family' and he figured I would eventually take him back.
Ex and I have been getting on ok recently and have settled into a routine with DC.
It was 12 yo dd's birthday during the week and as it was his day to have dc he asked me to go up after work to cut her cake.
When I got there his mum and dad were there too and we all sat at the table chatting and had some food. Dc were happy and I left after an hour pleaded that we had come so far.
Yesterday my 12 yo was having a sleepover with her friends to celebrate her birthday and as the weather here is so good, I bbq'd fit them.
I took photos and sent to exh, mil and my mum who lives abroad.
I got a text back from mil saying how wonderful photos were and was (stbexh) working the bbq?!?!
Now I froze, I did worry that she would see exh and I joking and friendly and think we were getting back together but this txt has me concerned.
It could be that she's 'old school' and thinks only a man can light and cook on a gas bbq I really hope that's the case! or she's deluding herself that I will take him back after everything he's done to me.
How do I handle this? I want to keep her involved with the DC, she says she loves getting the photos and she is really close to them. I don't want her to resent me either for not being willing to take him back.

I'd send a jokey text back:

Thanks for the text.
All the cooking was done by me!
Woman, meat, fire...
Was a good day, Dd had fun.

Don't mention him. No point, she knows what is happening. You can't control what she wants to happen.

I agree with PP, keep it lighthearted for the dc.

Thank you, that's more or less what I txt.

She needs to know you're not going to get back with her son; he was given many chances and let you down once too often. You're working at a civil atmosphere with him because he's father to the DC, and you want them to have a good relationship with their entire family. You appreciate her still being friendly with you in spite of the split. And finally you're not going to get back with her son; he was given many chances and let you down once too often. (All the above best communicated face to face, IMHO)

I would take a step back, she doesn't need to know everything that's going on in your life. Your personal life is none of her business. Just ignore any messages like that, and keep contact about the children

Thank you, she had closed herself off from me after the split and the realisation I wasn't going to take him back again.
I worked hard to keep up the lines of communication through text as any face to face meetings have been awkwardly polite.
She lives close to me so is privy to the comings and goings from my house too.
The dc don't want to move so I'm trying to be nice and respectful to her as their grandparent. She also does me a huge favour by keeping youngest for an hour three days a week until I get home from work. She really is a good grandparent but feels that women should turn a blind eye to their h's indiscretions like her own mother did.