More next gens!
I think Pinkie is one of the only characters that I have changed drastically from the canon of the series finale, but only because I don't really dig Pinkie x Cheese Sandwich all that much. So in my AU I made her and immigrant AND a princess, and took a little more time to explore her adventures out of Equestria

1)
Doing her job as Official Friendship Ambassador for the yaks, Pinkie Pie fell in love with Yakyakistan’s culture: its music, its food, its customs, even its harsh weather. Perhaps because it somehow reminded her of the rock farm she grew up at.
This and her growing friendship with Prince Rutherford turned her trips to the north into a routine of sorts. She would spend a few months a year, usually in the summer, living in Yakyakistan with all her new yak friends. Twilight even consulted her frequently while writing a book about yak folklore, as she had become a respected figure among them, with her title of honorary yak and all.

2)
Spending time with Prince Rutherford made her realize that they had a lot in common. They both enjoyed loud, chaotic music, dancing, celebrating, bakery. And sharing each other's experiences with their own cultures, they never ran out of things to talk about!

They never really considered it as "dating", but they did realize, practically at the same time, that they had fallen in love. Rutherford proposed to Pinkie rather quickly and she had to take some time off to think about it, but after some long spa talks with Rarity and some dinners at the Apple's, she figured she should follow her heart (and her Pinkie Sense™), and came back to Yakyakistan the first day of spring to say yes!

After the wedding, Pinkie started to spend more time in Yakyakistan than in Equestria as she settled down with her new husband, but of course she visited as often as she could to meet with her good old friends. Sometimes she even brought Rutherford with her! He never liked spending time at Ponyville all that much, it was too hot and too small for him, but he wouldn't say a word about that because he enjoyed seeing Pinkie smile more than anything in the world.

Speaking of: Rutherford is the biggest himbo. He's a loving husband and a caring ruler, although sometimes stubborn and not very bright. Also you don't want to meet him when he's angry, don't ask what happened to the last guy who tried to talk down to Pinkie for being a pony.

3)
Before your eyes, the very first pony-yak hybrid: Tambourine! (Or Tammy, or Tiny, or TamTam, or Tummy Tumps, or whatever other pet name Pinkie has used for her over her life)

She shares a lot of her mother's bubbly personality: she's loud and uninhibited, and a lot of fun to be around.
She grew up in Yakyakistan for the most part, visiting Equestria with Pinkie as she grew a little older. She speaks both pony and yak, and is in close contact with both sides of her family.

Right now Tammy is living in Ponyville, attending to Princess Twilight's School of Friendship, were she became friends with Luster Dawn. Her fun personality as well as her mother's reputation helps her a lot when it comes to making new friends, and she generally feels very welcomed in Equestria, but deep down she's still a little insecure about her place in the world; too small for a yak, and without any horns, but too big for a pony, and without a cutie mark.

4)
Faimly portrait! Also a sketch for size comparision. Tammy grew up to be bigger than the average mare, but not robust enough for a yak (she's roughly the size of Big Mac or Shining Armor).
She grew up very fast too. She was the size of her mother by the time she reached her pre-teens! You'd be surprised by how strong Pinkie has gotten just from carrying her around when she was a baby, and she didn't even realize until her friends pointed it out. She may not be as young as she used to, but she can still push a confetti cannon around like it's nothing.