Zimbah, it sounds as though she is now bored with potty training, she knows she can do it but at the moment is choosing not to. Probably things are a bit unsettled at the moment, she hasn't a clue what it will be like having a new sibling in the home, and mummy isn't quite the same as usual, tired, a a bit cross maybe when she has an accident or refuses to go to the loo. It is normal behaviour at her age to push the boundaries to see what she can get away with. Don't underestimate how emotional upset can affect a child's potty training, if they think you care very much about the accidents they will wet on purpose, even after flatly denying they need to wee.
You could try 'racing' her to the loo, saying ' I need a wee before we go out, I bet you can't get there and do one before me' and of course you let her win and get there first. I think constantly asking if she needs to go will result in her refusing on principle, so you could just start a routine of going to the loo and handwashing before meals, say, and just before going out, or just before a fun activity where she will become so absorbed she will not want to stop to do a wee. Make it a statement rather than a question, 'do a wee and then you can go on the swings'. I know it's hard, but the more agitated you are, the less progress will be made!
mayson, think about what could be going on in your sons life that might be causing this, I think it may have an emotional cause, especially with the tantrums. Suggestions are family bereavement, moving home, moving school or nursery or starting at them, bullying, new sibling, siblings moving away, separation/divorce or parents new partner in their life, parents or siblings seriously ill, anything that has caused upheaval and upset.
Quite often young dc who are experiencing unsettling life events over which they feel powerless and distressed, find some element of control through where they do a poo, no-one can make them do it, and make them do it in the toilet. They choose when and where to do it. It's a shame that the health visitors have been no help, perhaps you would do better taking your son to the GP on the pretext of whether he is constipated, and rule that out first but do explain about the tantrums and soiling at the same time.