INFO: how did your wife ask?
Because I feel like this situation is probably very dependent on context and behaviour.
Your mom sounds like she was surprised and annoyed by the way you responded, and she stood up for your wife - to me, that's a clue you might be the one in the wrong here.
If your wife was nursing or is still recovering from the birth, she might struggle to get up. And it's also possible she was merely being friendly/chatty and asked politely for another tea. e.g. if a family member brought me tea that was very sweet, I might politely ask for another, and if it was then too cold, I might also ask (more politely and probably a bit apologetically for inconveniencing them) "sorry to be a bother but would you mind please warming it up a bit for me?"
It's all about the relationship between the people and the tone you're asking in. And if the conversation was like the one above, and you butted in (as someone half-listening while they worked) and snapped at your wife, then YTA.
If your wife was demanding the tea or bossing your mother around or being rude, then yes, NTA. But there's not enough info in the post to be sure which was the case.