I don't see any reason that both issues can't be addressed simultaneously actually. It isn't acceptable that your DD is being driven from her home on weekends to escape the situation. I would move the rooms around and then you are free to focus with the problem at hand without worrying about the effects on DD.
Focus being the operative word really. In addition to professional help and advise these children need to be focused on positively.
Whatever the root cause of the issues, what they are begging for via these behaviours is to be centre of focus for however short a time. Children who have suffered damage of some sort don't tend to differentiate between positive and negative attention, from their perspective, when dad is punishing them he is focused entirely on them. Not busy with work, or the baby, or family life in general. Just them. For a moment or two.
Please try and empathise for a minute OP, with exactly how troubled and inwardly distressed these children must be to crave even punishment to make them feel secure.
Do not punish or chastise them when these incidents happen. Quietly and without fuss clean it up, don't ask them why they have done it or why they didn't tell you. They do not have the answers to those questions!
Whenever they do use the toilet correctly, or even when they come and tell you about an accident instead of hiding it, make a fuss! Tell them how pleased with them you are that they have been honest or been to the loo. Teach them that they will get positive focus for doing the right things!
Do they do these things at their mothers? Have you any idea how she deals with it if so? Consistency between homes is always a good idea where possible.
Do go back to the GP, ask school of they have similar issues there.
These kids are metaphorically screaming "LOOK AT MEEEEE". 