Playful Parenting by Lawrence Cohen will give you lots of ideas for creating playful I love you rituals and a more playful atmosphere to encourage cooperation during power struggles. He even discusses your exact situation and how play can help. It's all about connection and creating quality time with your child. Here is an extended
preview which is long enough to give you the basic theory and a few examples. Reading the book will give you more examples that cover more scenarios but may not be necessary if you are super busy right now.
Another book I really like is Becoming the Parent You Want to Be by Laura Davis and Janis Keyser because it has lots of real life scenarios of discipline techniques that connect with the child. Their toolbox is summarized in 13 pages 226-239 and may be a good reference point for a busy parent with a toddler and a newborn. It is a reference book designed to pick up and read a section at a time rather than cover to cover. If you have it already it might be worth skimming the contents for other sections that might apply to your situation. My favorite sections are part 2 children's feelings, part 4 difficult behavior and chapters 23-24 on social learning.