Job withdrawn after I asked about flexible working

I have been made a job offer and signed a contract. I was due to start in March. I asked the company if they offered flexible working and they asked what I was thinking. As it was not a regular pattern I sent them a list of days where I would like to leave early to pick my children up from after school club as my husband works a shift pattern involving some nights. I stipulated that I could be flexible around this if the business required me to attend meetings or go to other locations. They called me in for a meeting and I asked about their concerns and agreed to work the core office hours they stipulated. They have since withdrawn their offer, stating they don’t believe I can commit to the travel requirements. They have offered my one week’s pay in lieu of notice and said I can appeal to the Managing Director. Is this discrimination and is it worth fighting? I turned down two job interviews on the basis I had this job.