After marrying again, can I stay several nights in a row with my new wife?

The Sunnah gives a new bride some initial nights before the normal rota begins, and this is not counted as injustice. The Prophet ﷺ explained: “It is part of the Sunnah: when a man marries a virgin while he already has a wife, he stays with her for seven nights, then divides the rotation; and when he marries a widow, he stays with her for three nights, then divides the rotation” (Sahih al-Bukhari 5213). Explain this right gently to your existing wife so that she understands it is Sunnah, not favouritism. After that period, begin a fair rota (turn of nights). For your particular situation, refer to the religious affairs office. See fiqh of polygyny.