Since Ponyville seems to be a small farming town, and Equestria is not as technologically advanced as earth, their communities are probably more close knit. My grandmother has told me stories of her childhood when more communities were like that.  
Kids could go out and play with their parents having no idea where they were and everyone just kind of kept an eye on each other.

Some Colt/Fillie: My mommy got married! and now I have two mommies!  
Dinky: OH YEAH!? WELL GUESS WHAT?! I HAVE 100 MOMMIES!  
every single mare in ponyville in 1 dogpile

Oh well, headcanon: We don’t actually know Dinky’s mother yet, but I suppose she’s a unicorn.
 
Dinky and Tootsie are twins, and she, Tootsie, Sparkler and Written Script are siblings. Script is the oldest.
 
We already know that she’s friends with Noi. That makes Carrot Top both one of the best friends of her big sister and the big sister of one of her best friends.
 
Also, Carrot and Script are a couple now which is canon, too.
 
No wonder that Dinky likes to spend time with Carrot Top. Also, that way, adventurous Dinky was the first in the family to see the Crystal Empire.
 
Millie is her occasional foalsitter.

@Background Pony #1C7F  
Headcannon: They’re all Time Turner’s companions. Whoever isn’t out saving the universe has to watch Dinky because Derpy

anti-scootaloo xD

>Derpy has to work long hours delivering, often away from home  
>Everyone just helps keep an eye on her, because Ponyville

Just pointing this out here, but she also appeared with Coco Crusoe and Sassaflash too.

@Background Pony #EBAF  
Dangit, now I want to see that in the show…

She must go through a lot of baby sitters.

Head-canon: There is no “Dinky Hooves”. All of the fillies you see there are changelings infiltrating Ponyville. Not particularly bright changelings, because they all use the same pony model. Fortunately for them, Ponyville’s ponies aren’t very bright and haven’t caught on yet.

 

@Wiimeiser  
My heacanon is that Dinky is just an intellectually- and emotionally-mature filly that relates better to adults than children, and thus spends a disproportionate amount of time with older ponies as a result.

@Background Pony #EBAF  
That’s utter poppycock! You didn’t see nothing.

What if there are an army of lilac unicorn fillies with blonde manes and golden eyes?

Let me quote a previous comment of mine:  

 
I think that’s the technical explanation at least…

@Strawberryjuice  
She has so many moms that I think she could just spend the night at anyones house :o

Geez, filly, leave some mom for the rest of us.

She’s a foster kid. She goes through a lot of families.
 
And Carrot Top draws a lot of short straws.

It takes a herd to raise a filly.

She’s the daughter of Ponyville.

So which is her mother, and which are ponies she just knows?

I think this means that everypony in Ponyville is Dinky’s family :o
 
At least 3 of those screencaps have Carrot Top/Golden Harvest nearby so maybe she’s related?

Does that means she doesn’t live in a house?