@lucy901123, it would help to know what your level of experience is, and how severe the learning difficulties are.
If it were me I wouldn't rely on being able to set anything up - background, flash, posing or anything. I would try to rearrange furniture or get people to sit where there's good light, though, and concentrate on capturing natural reactions. The animal handler is going to be in the way a lot, so make sure you're on the opposite side from him. The subjects are likely to remain sitting - make sure you get down to their level.
You may well want wider angle than 50mm, and you may find that f1.8 is way too shallow to get both animal and subject in shot. Experiment before hand to work out what you'd need to say get someone's lap and face both in focus. You may also need a high shutter speed (>1/250s) to freeze animal movement but may be better off just timing things carefully. Don't be afraid to bump the ISO right up. I'd shoot in manual so I could control both aperture and shutter speed and ensure that neither went too low.
I'm guessing you're not familiar with flash, in which case this probably isn't time to start unless you have time to practise. If you do have time then work out how to use automatic flash on your camera, bouncing it off the wall & ceiling behind you. That could solve a lot of problems.
One tip I was given for home portraits where you don't know what you're going to find was to ensure that you take lots of voile fabric. Then you can put a couple of layers over any windows or patio doors which are letting in direct, harsh sun - unless you want to get creative with shadows. Then you also have the option of using it as a plain white / light grey backdrop.
I'd also take some reflectors to bounce some light into faces. You may be able to just prop them up and leave them. Large pieces of white card will do the job.