To be getting annoyed by DPs nans comments?

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So long story short..
Me and DP have been together for over 4 years and have a 3 month old DD.. My DP is very close to his GParents and they come round VERY often, even more so since DD arrived.
I'm beginning to get very irritated by DPs nan making silly unnecessary comments every time she is round. If I'm holding DD it's "oh you're spoiling her too much", "put her down, you'll regret it!", and then the one that winds me up the most is when she's talking to DD saying "ohhh they're starving you ain't they, they're starving you", "are they starving you??" If she makes any sort of noise it's "oh maybe she's hungry, have you fed her?" Obviously she's fed regularly and isn't being starved and she's 3 months old so obviously I'm going to be holding her regularly.. I just don't understand why she makes these comments.
The thing is I get on with her really well but these random comments are really starting to piss me off because I don't understand the need for them at all! AIBU to be getting so pissed off?? She's been asking all day to come round to see her and I've been making up excuses because I really can't be arsed with the comments!

Put the latch on verytime-its not on for her to just stroll in whnever she wants

My dsis has a key to mine but has never once used it to come in when she pleases

Your DP needs to stop her coming round so much. 3-4 times a week is ridiculous and would drive me nuts. She clearly has nothing to say when she comes round either if she just has to repeat banal idiocies the whole time. Tell her the key is for emergencies and say no more when she rings to say shes coming round.

God who does that! Remind her that it is for emergencies, doesn't have to be nasty just a "sorry to say brenda but you nearly caught me in the buff/us having a shag/me indisposed the other day, could you just knock from now on please" text her if you can't say it face to face. You need to work on standing up to her though. Practise saying no to her at least half the time she asks to come over. That is way too many visits and if your DP doesn't have your back unfortunately you need to be setting your own boundaries. These are skills you will need as a mum, even if it's hard now.

My MIL is a bit like this, the baby's not even here yet but she's constantly telling me what to do already.

"You won't forget to give the baby enough food, will you?"
"You will check that the baby is warm enough, won't you?"
"You will clean the dog's feet when it comes in the house, won't you?"

To which I normally just go 'hmmm' but occasionally just tell her to stop depending on my mood. I sometimes also just tell her that I'm just going to leave the baby to her to bring up instead (in a jokey way, it does make her laugh and stfu.)

I get that she's worried and I get that it's how she shows love, but that doesn't mean I have to put up with it.

Sounds like typical nan talk to me. Let it go over your head.

My Nan used to say to DS as a baby...

“What are they doing to you..”

“She’s a cruel mummy not doing xyz isn’t she...”

“What are they feeding you!”

None of it taken with any offence. I know really she thought I was doing a fab job.

I'd change the locks and tell your DP if he dares to give her another key it is curtains. The old MN mantra, you have a partner problem.

My husband's grandmother used to tell me our cats would steal our baby's breath. There are times in life when it's better to choose your battles; this is one you shouldn't choose. Just ignore. No one is paying any attention to the silly things she says.

Time for your DP to have a quiet word, my FIL did this sort of thing to me (told me off for holding my crying babies etc) and it is why we stopped seeing them so much.

My first born is super independent, happily ran off to kinder and school without a backwards glance lol, my second is only 2 1/2 and much more clingy - I have raised them both the same. You can not spoil a baby with love.

I’d put the latch on each time you are home and when your DP says something about having to knock “your Nan walked in whilst I was asleep.” “Your Nan walked in the house whilst I was having a poo” “I wanted a nap without your Nan letting herself in”

It will make her realise that she can’t just walk in anymore without you having to have an awkward conversation and will make him realise that’s you are serious.

Create a new habit of putting the latch on and only being available once a week.
It is either that or you will have to tell her how much her constant criticism is hurting you and damaging your relationship with her.
You really ought to do both, but you know that already.