I will agree to shoot there when the client pays for the shoot and yet still trusts in my ability to produce a great image and a great product. There are no bad situations that cannot be adjusted for with a bit of creativity. 

As a professional photographer you need to control the situation 

You need to bring lighting backgrounds and all the necessary equipment to get the job done right 

I see too many photographers relying on available lighting that is why you’re not getting the best results 

I would agree to scout the location, if possible, and take a photo at approximately the same time as the scheduled shoot. I would then take the photo and discuss it with the client and show the weaknesses, but also have to options on what could be done or possibly an alternative location. If you would need to rent additional lights/equipment, etc. tell the customer the additional costs involved. Sometimes when additional costs get involved the customer’s insistence changes. 

You have to be comfortable with what you are shooting, including the "set."  In my commercial photography practice, all of my shoots are on location.  I do bring studio strobes, and I can bring backdrops if warranted.  The only things I shoot in my studio are products, and often, I need to shoot them on location as well.  It can be challenging. I admit..Rick  rcm Imaging

I recently took on a business shoot for a team of 5 at high noon at a local park because that's what suited their schedule.  A few years ago I would not have had the confidence to do that and would have tried to persuade them to book at a later time or referred them to someone else.  I don't want my customers upset with me for crummy images.  Over time I have been working on techniques such as flash and developing an eye for locations against buildings, under trees etc so I was able to pull off this job.  There was a particular fun shot they wanted at the end of the shoot out in the blazing sun and I did explain that I would take it but explained how it would turn out.  We had fun giving it a go.  A few days later it occurred to me what I could have done to make those particular shots more successful.  I will be even more confident next time!

me personally, I always try and scout the location and if so I will contact the client with my concerns, if they still persist I will explain why the location wont work.

What type of session was it... large group, individuals, etc... There are so many things that can be done.   Individuals, using GOBOs to block unwanted light,  control the background with exposure and adding light on the face to match.  Large groups, do what they want and if you can move them 50 feet away that might be better lighting do that.  Set your lights before hand, so you can just repose and go.  Hard to give more without more info.

Don't expect clients to cater to your limitations. Take a good hard honest look at the things you struggle with and learn how to overcome them. There are literally thousands if not millions of YouTube videos that show you how to shoot portraits in less than ideal conditions. Start here: https://www.youtube.com/result...

I have turned down jobs for that exact reason. You run the risk of losing future clientele if you put out substandard work to appease that one client.

Make it work. Make it look great. That's the difference between pros and non pros.