British Airways BA stopped me in last moment at time of family emergency from travelling and not responding now Internet

 Hello team, My actual date of travel was on 19th Jan to my origin country and I have chosen British Airways (BA) for travel as it was a family emergency for me in my origin country. But the airlines has stopped me from going at that last point of time where I am alone with my 2 year old baby. The person over there told me to wait while was checking in and he went and enquired a couple of members and again finally to the manager and then told me my baby can't go n I can go. He also said that I can leave my baby there and go. How is it possible to go leaving baby alone in airport. The reason they told us is as British Airways is through London they need a proper visa. Actually my baby resident visa expired out of which she is on visitor record and we cannot apply visa for her inside Country but have stay permit till 2018 issued by government. Also we have shown that to the manager and she didn't accept it saying not useful. We have to travel to our home country and do there. And she asked us to apply for UK transit visa.

So the manager over there has postponed our tickets to March 1st charging me 550$. Without having a choice I just kept quiet and returned my home. But after that I checked the whole website of BA. No where in the website it is mentioned in the website about having UK transit visa and I also found various other rules and regulation for having visa for countries like China and Arab. I contacted customer service and the people in that are very rude. They are asking me to go to embassy and check the rules and then only book the ticket. As London is main transit for BA I think it's responsibility of BA to put the condition in website. And the employees of BA doesn't even what exactly this is and when I ask them they say they don't know and its my fault. When the employees of BA doesn't know nor the website provides the proper information how will the customer anticipate such consequences.

I requested for refund of money and postpone charges because I can go emergency atleast now in other airlines. From my side I have applied for UK transit visa but somehow they rejected it. Being helpless alone , having emergency I have been unable to travel and requested for refund. The people are rude and they are saying they can't refund. I complained in customer relations twice. I have not received any response from them till now. If they give me back my money I can just travel through other airlines. I am just asking for refund to travel myself in other airlines. They aren't understanding my situation not even showing minimum courtesy. Please help me.