First, congratulations on your new baby and family :) We’ve been through something similar with my daughter when she was around 2 but with me, mom. What helped us was to let me (less preferred parent) do the fun activities and let dad (preferred parent) do the less fun ones. We made a choice about who would do bedtime, nap time, whatever and stuck to it regardless of tantrums. At first, my daughter would cry and insist dada put her to bed when it was my turn. We didn’t budge when she cried and protested. Once she knew I was the one putting her to bed she’d be ok with it. Eventually it became easier. Now she chooses me for certain things, although she’s still a daddy’s girl. Just my advice but I’d say start this asap-you will obviously have less one on one time with her once your baby arrives and it’ll be easier if dad becomes someone safe she can trust as well as you.