"I said he is a 43 year old man I'm sure he can organise his own lunch"
This is how it started - why did you feel the need to address this with her? If you have an issue with the situation, talk to him. I would get the ick with a man who allows himself to be babied by his mother, but it is him you should talk to.
"she said "yes but me I love my son" (emphasising with her voice that it must be in contrast to me)"
She understandably got defensive, so went on the attack
"I began to lose my temper a little so I said "do you warm some milk for him too?"
You escalated it further instead of de-escalating and walking away. Why did her comment get to you - why is this such a raw nerve for you? Do you doubt how much DH loves you? Do you see her as a rival for his time and affection?
"and she said "listen it's simple, I am the first woman of his life"
She escalates yet further in response to your attack. She is also showing her rather warped attitude to him: over-possessive and unable to let go.
and I said "true but I will be the last".
Witty, but also too mean.
Then she started crying and ran out of the room.
Unsurprising given how the argument ended.
Advice: don't get into petty squabbles with MIL as it just makes you look bad when she gets upset.
Separately, look deeply at what exactly you don't like about his relationship with his mother. Is it that you don't like him behaving like a child around her? Are you fed up with the amount of his time she takes up if she is going round there every day? Or are you irrationally jealous that he spends time with another woman? Would you feel differently if it was his father that he was spending so much time with?
Talk to him about it, not her.