I found a stray (female) about a month ago. I notified all nearby

File: Two-Dogs-Better-Than-One.jpg (119KB, 700x405px) Image search: [Google]

119KB, 700x405px

I found a stray (female) about a month ago. I notified all nearby shelters/hospitals and haven't received a response so I decided to keep it. I have a two problems.
Problem 1: My dog (female) will not tolerate the stray unless the stray is crated. If the stray is crated, my dog can walk by and sleep next to the crate with no issue. She occasionally tries to sniff the stray's butt but it's kind of hard cause there's a crate. Normally, my dog will bark/lunge at other dogs (ex: on a walk). If I put my dog in the backyard and let the stray roam the house, my dog will bark and pounce at the glass door, as she can see the stray is out of the cage. The only place the two dogs can "coexist" is on the car, but that may be because they're both dizzy or something. If I try to walk both at the same time, my dog barks/lunges at the stray as if she would towards any other dog. How do I properly integrate the stray into my house so that my dog won't bark/bite her? The stray seems to be indifferent towards my dog with the exception of problem 2.
Problem 2: The stray does not like my dog being nearby when the stray is being fed. If there is food inside the crate, the stray becomes extremely defensive and will bark loudly at my dog if my dog comes close to the cage. The stray has no issue with me taking the food away though.