YABU to interfere. I had pretty much the exact same upbringing as your DN. Both my parents worked since I was a baby, until my mum had my twin brothers when I was 5. In fact we lived with her until I was 2 and my parents found they only place. My Nanny brought me up, and yes she probably fed me all sorts of crap because that is what grandmothers do, and God bless the lot of them!
And my mum was probably earning a pittance in a crap job, as was my dad, just to earn enough to keep us going - my Dad is Spanish and when he came over to England he hardly spoke a word of English, and had to learn the language so he could get a job!
Even after my brothers were born, Nanny still had a huge part in my upbringing as my mum found it hard with my DTBs who were very demanding.
I can assure you that despite eating lots of crap, I do have a pretty healthy diet, and turned out okay, and am grateful for both my parents for working their fingers to the bone to get a decent living, and I know my mum is grateful to her mum for bringing me up!
Frankly you sound very judgy. How can you possibly understand everything about their life, their finances and the way they are raising their child? I could turn around and say it is cruel to try and force a routine on a 3 month old, but I won't as I have no idea if you are or not. Routines are not always necessary for a healthy and happy childhood.
By all means feel free to serve up healthy dishes and snacks, perhaps if he sees you enjoying them, he will be tempted as well and you can give him some good healthy eating habits. But don't make him feel bad if he wants to have crap and doesn't want to eat the healthy stuff as this is the quickest way to induce food related neuroses!
Oh an my brothers have and always had terrible diets, they eat no fruit, only ever eat sweetcorn and they have always been super skinny but extremely healthy and fit, and have rarely had a day's illness in their life!
And FWIW, I did have an Aunt like you, my mum's eldest brother's wife. She had 2 DDs both older than me, and they bullied me, and my Aunt was mean to me when me and Nanny went to visit. As an adult, I cannot stand her she was such a bitch to me, I got seriously uptight when my mum insisted I had to invite her to my wedding, thankfully she declined.
Don't allow your DN to think of you in that way