Property and kids dispute

Hi,

I am hoping for some advise

My ex de facto partner and I seperated after being together for 6 years. She moved out of the house which was in both names.
At the time we had 1 child togther and she took him.
Due to some mental health issues I took our son back to live with me, she took me to court and we signed a court order stating that he would live with me. Since then we have had another child together, even though we we seperated, we were thinking of getting back together, the second child is now 9 months and he too lives with me, she is not happy about this but due to her mental state (She tried to kill herself a number of times and DHS are still involved) I took the youngest from advise from DHS. We are still seperated but she now but she has changed her mind over the eldest (Now 3) and the youngest.
Is she allowed to apply to the courts again over the eldest considering she signed an agreement with the courts that said he would live with me? If the courts would not consider this, what are the chances they would split the 2 boys up if she tried to have the youngest live with her


Finally, the house was in both our names when we split up and she verbally told me that I could keep it and she did not want anything for it. At the time we had $250 K owing on the mortage and that was 2 years ago, she recently (3-4 months now) signed the title over to me and the mortgage into my name only. The banks have approved the new loan. She is now thinking of changig her mind and wants money for her share (Even though the house is in my name and when we were together she did not work but looked after the eldest). If she signs over the house can she then stil go to court even if it is 2 years after we broke up and 4 months after she signed the house over to me?