You are 100% right, but please be gentle with her over this. She wants to show her love for the baby and will be a huge asset in the future.
You (and your baby) are very lucky to have her.
I can relate. My ex's mother was a bit overbearing and I did resent her a little, with her nonsensical pregnancy advice and superstitions.
However, I soon came to realise that she was head-over-heels in love with our baby from the moment she heard I was pregnant.
She and my FiL became my children's staunchest supporters (better than my own parents) and all-round wonderful grandparents. Your child too will have this fantastic advantage in their life.
So in your place, I'd swallow my pride and go cap in hand and actually apologise to her. Maybe take flowers. Just you, woman to woman.
You'd be doing this not for her or you, but for your child.
Don't apologise for having a different plan, but for 'jumping down her throat' about it. You want her onside so a bit of grovelling is a small price to pay.
You don't have to mean it!
Although it sounds as if her feelings were hurt, which is a shame. I wonder if she went home and cried.
Say something like 'About the other day, I'm sorry for biting your head off. We know how we want to handle things and I think it might be a bit different from how you did it. I'm sorry for overreacting.'
There may be a hug and a tear or two, all good.
Then you can butter her up with 'I can't WAIT to see your face when the baby comes!' and hopefully lead into a lovely conversation about the wonderful times you will all have.
Remember that after the first few months, depending on how you're feeding Junior, Gran will be able to take over now and then to give you a break, as she has promised. Take my word for this: by then you will be DELIGHTED.
Also - things might not turn out according to your plan. I don't mean anything will go wrong, but circumstances change and you might find you need to adapt a little. Having Gran ready to step in would be a huge help.
Anecdote time -
In one of my later pregnancies Gran happened to go with me for a scan. Back then they were strict about who was able to go in with expectant mothers; only the baby's father or the expectant mother's own mother were allowed.
I told the technician Gran was my mother so she could see the scan.
Gran cried for joy the whole time! I honestly think it was one of the best moments of her life.
This was before photos were given out but if they had been, I would have handed mine over to Gran without a second's thought. She was totally worthy! Your child's Gran will be too. Cherish her.