Most dogs don’t like hugs. If your dog is ignoring her while she attempts this, that’s his way of sharing he doesn’t want it. Please, stop your child from hugging your dog. Teach your child appropriate dog interactions, instead. If you need help, find a good, balanced trainer who can train every member of the family, including your child.
Also, male dogs do not go into heat like female dogs. Please do research on basic biology of canines.
PLEASE wait until your existing dog is an ADULT before bringing another puppy into the home. PLEASE.
Don’t put peroxide anywhere on your cat. Until you see your vet as suggested by Sarah, use a warm wet washcloth.
Honestly, I would consider them all unsafe. Cats have delicate respiratory systems. That said, things like tea tree and eucalyptus WILL cause your cats very significant health problems.
But seriously. Toss the EOs.
Hot flashes? I don’t know that this is something dogs experience. She could be feverish, though.
I’ve never had kittens, so I cannot speak to this part of your question. I do know quite a bit about dogs, however, and I would NEVER suggest getting two littermates in dogs. Ever. This causes some serious developmental issues – littermate syndrome and dog aggression are but two of them.
Invisible fences should never be used unattended…and every person I know with one ends up with a real fence eventually. THAT SAID I know a number of hound people who hunt train their dogs and use e-collars for distance training. I would encourage you to look into field/hunt training.
Get her checked at the vet, first and foremost. She may have underlying health problems from this, and you want to get that cleared ASAP.