It seems like you are in the middle. It is difficult but possible. You have to include both of them in activities together as well as individually. There should be couple time and child/parent time. One should not overshadow the other. Give your partner time for romance so that you can be a couple without being a parent. She will appreciate a candlelight dinner without no talk of children. Then she may not feel as pressed when your attention is on your daughter. Have firm boundaries in your home so she sees that you can set limits that respect her feelings. Always take her views into account even if you don't agree with them. Give her reassuring words when you think she needs her opinion valued. Don't act as if your word is final but use a process based more on a consensus when you can.
Your partner wants to feel heard. That goes a long way. She always wants her time. Sometimes you have to be a partner over a parent. There are times for everything. Nurture the relationship routinely. Try to listen to her complaints and work on compromises.
Please press accept; this is the only way I am compensated