Actually, I strongly believe that the issue ALWAYS lies with the parents, who are supposed to be the Adult in the relationship.They are the ones responsible for the kid and they are the ones that give the kid the pet, or the means to obtain the pet.
Perhaps you should get the parent to read this Forum!
Bad parents will just stick their kid in front of a TV, or give them what they want, when they want it...all for an easier life. When those kids hit The Real World, many struggle and cannot cope as a consequence.
Good parents are totally involved with what their kids do and offer whatever support is required, when it's required.
For your situation, the Betta needs to live in a bucket, whilst you remove the plastic plants and rinse out the substrate, to the very best of your ability, in tank water. Then put just enough substrate back in the bowl to cover the base. You need to buy a load of basic pondweed (Elodea) to put into the bowl. This will help oxygenate the water, manage Betta waste products and give the Betta some security.
You can then put the Betta back in the bowl and keep up with water changes and try to keep it warm.
You then need to nag your parents to get what they should've got in the first place...a proper tank for the Betta. Your sister's getting nothing but bad lessons from her experience and living creatures are suffering along the way, with you caught in the middle. This isn't good for you, your sister, the fish and, in the long run, your parents.
I suspect your kid sister isn't really interested in fish and only wants what you have...because that's what siblings do.