It's human nature to get wrapped up in something you feel passionate about - but it can mean that you develop a distorted view of what motivates you.
Social workers, by definition, have to have a deeply felt intution for humanity - but they can get so deeply into it that they see things that are simply not there.
Your reaction to talking about your mum is - as has been advised by many posters - perfectly normal, but this lady is determined to see into it a level of grief-related instability that is simply not real.
When life gives you lemons, make lemonade.
If this lady stands between you and fostering, and she wants you to apply for counselling - show willing and co-operate. You will be linked with any foster children far more deeply and for far longer than you will to this slightly unhinged individual, whom you must view as a means to an end.
Good luck - you sound perfectly suitable as a fostering family - play these ludicrous games if it gets you where you need to be.