Is the husband sinful if he refrains from speaking to his daughter and spending on her until the lawsuits filed against him by his ex-wife are concluded, knowing that he wants to give her her legitimate rights and deferred dower?

As for what transpired between the husband and his divorced wife, the Sharia judiciary will decide it. The daughter's maintenance is obligatory upon her father from her own wealth, and he can appoint someone to deliver it to her. Developing the daughter's wealth through legitimate means is obligatory upon the father because he is responsible for her. There is no justification for cutting off communication between the father and his daughter via phone or other means, as severing ties of kinship is forbidden, unless it becomes impossible due to a problem beyond his control.