Looks like Sophie is going into her first heat. Slimy brown discharge is the first signs of the cycle. The first cycle is usually triggered by body weight; if she is 35lbs there is a good chance her body is readying up for heat. Genital and teat enlargement is clearly seen around day 7. I guess Tucker is a male; he is your best bet for confirmation. Males will know a few days earlier than the actual physical signs start showing up in the female.
Diapers, panties, napkins, whatever butt-padding works for your pup is mandatory for your and your dog's comfort. Don't be swayed by she wants to go outside, so you need to take them off. During heat some females experience drip peeing; mine did and I learned the hard way. Luckily for us, we have tiled floor and no carpets; so I could just mop up with vinegar to take away any unpleasant odor. Also in India we have the opportunity to air out the house year round; it is never too cold. The trick is to have butt-padding handy and change 4-6 times if necessary.
Expect mood swings, appetite changes, thirst or lack of it and clingy behavior. Pamper Sophie and Tucker. They are going through a tough time.
The rest I have covered in the other thread.