cat scared of new puppy

We just adopted a new 6 month dog and our 5 year old cat will not come out of the basement. We also have a small kitten that gets along with the new dog and a 6 year old lab that gets along with everyone. 

The 5 year old cat has always been very scared of about everything. We used to have a small boxer mix that died recently and we believe that the cat was peeing all around the house because of the stress brought on by the dog. Since that dog passed she has stopped peeing. We are worried that if the cat is scared of the dog then she will start to pee again. We also don't want the cat to spend the rest of her life in the basement.

Some members of my family think that we made a mistake getting the dog and say that if the tension isn't gone by the weekend (it's wednesday now) then we will take him back, but I keep trying to tell them that the whole process takes time. We are also currently potty training the dog and people in my family are worried that it isn't happening fast enough, but we have only had the dog for 3 days! 

Please help!

Can you keep them separated by a door at first, putting their food dishes next to the door on both sides, so they can get used to one another by smell first?. Don't just let your cat hide in the basement all day or she'll probably stay there without the chance to get used to the puppy.  Of course you want to make sure you still give your kitty lots of love and attention (extra love actually, so she doesn't feel the need to be jealous) Then move on to a gate if possible, then having both supervised in the same room. It's important for the puppy to learn that the cat isn't just like another puppy who will automatically want to play. 

My parents brought a puppy home where their 18-year-old cat Zou Zou was already living. This method worked for them, and after a while they were play fighting and licking each other. 

Thank you!! I will give it a try and let you know how it works!

Good luck!! It might take some time but it will be worth it  

This article may have some helpful information for you: http://www.thecatsite.com/a/introducing-cats-to-dogs 

Since kitty was there first; I think it's a good idea to focus on helping her be comfortable in her home.  Proper introductions do take time.  Your kitty needs safe places outside the basement that she can go to get away from the dog (cat trees, safe rooms gated off from the puppy).  A feliway (Comfort Zone) diffuser may be helpful since it seems like stress induced peeing; but those take time to build up and you need them to be where your kitty is; not just one room.  Also; please be sure her litter box is in a location that she finds safe and secure.  That will also contribute to inappropriate peeing. 

Good luck!