Er, shouldn't it be 吠えています instead of ないています? I'm not saying that the given sentence is wrong, because it's not, but I think 吠えています would be a better choice.

お店で3匹の犬が鳴いています。

お店で3匹の犬が鳴いている。

REMEMBERING SOME KANJI:

1. 店 - SIDE VIEW OF A STORE (THE TYPE THAT LOOKS LIKE A KIOSK) WITH A PERSON TENDING TO IT

2. 匹 - THE KANJI OF FOUR MINUS THE VERTICAL STROKE ON THE RIGHT (OR: "C THOSE LEGS? LET'S COUNT THEM!" - THE OUTSIDE PORTIONS OF THE KANJI THAT LOOK LIKE A "C" + HUMAN LEGS RADICAL)

3. 犬 - THE KANJI FOR "BIG" PLUS A SMALL DIAGONAL MARK ON THE UPPER RIGHT CORNER

4. 鳥 - COULD BE A PICTOGRAPH OF A BIRD PERCHING INSIDE A CAGE

5. 鳴 - "BIRDS USE THEIR MOUTHS TO CHIRP, YOU DON'T SAY?!"

What about "お店で犬が三匹ないています。"? Is it okay to write it like this?

Surely this should accept 1) は instead of が and 2) 店に instead of 店で? Wouldn't 店で imply the dogs are barking IN the store?

isnt san biki inu fine? rather than san biki no inu.

How would you say "three dogs are barking in the store"?

お店で犬が3匹ないでいます。