Hi OP,
I think a lot of dads feel like this to some degree.
I was talking to a father the other day who has an 18 month old daughter and whose wife has just returned to work after taking an extended maternity leave.
He told me that now he has to take on much more of an active parenting role he’s feeling very anxious a lot of the time.
When his wife was at home for those 18 months she naturally took on the role of main caregiver and so the dad now feels like he doesn’t know his daughter in a way his wife does, so gets anxious about if he is doing things “right” - which is his eyes means doing the same things his wife would do. This includes bath time, cooking for her, putting her to bed, general playing with her etc, he just gets anxious that he’s not doing it in the same way his wife would and so worries he is doing it wrong.
When I went back to work after my first child (when he was about 13 months old) my husband felt the same as you, and just got a bit panicky when he had to deal with our son and his routines without me there taking the lead as I had done during my maternity leave.
The fact that you still feel this way when your daughter is 3 years old may indicate you need to talk this through with someone professionally.
I can see why your wife gets upset and doesn’t want to talk about it with you - I think If my husband told me he didn’t like being a parent to our children I would construe that to mean that he didn’t love them, even if he swore blind that isn’t the case. She may also be scared that if you are not happy being a parent then it means you are going to leave them.
Nobody here can diagnose you as having some form of postnatal depression, but it does occur in men but it’s not spoken about very much - so it’s really good that you have reached out for help on here.
Perhaps you should speak to your daughter’s Health Visitor, they are there to support mothers with complex feelings about adjusting to parenting and difficult emotions they have when it comes to bonding with their children - so there’s no reason why she shouldn’t be supporting dads with the same problems.
It sounds like you are suffering from anxiety, so that is definitely worth talking to your GP about as there are lots of medications available that may help with this - which in turn will help you build a positive relationship with your daughter.
You clearly love her and your wife very much, you recognise that the way you are feeling is not “normal” (for want of a better word) so now you have accepted this, the time has come to do something about it before it snowballs further.
Well done for talking about how you feel on here - Now it’s time to take the next step and turn to the professionals to help you overcome these feelings 