I must admit that I am not a die hard gentle parenting person but I can completely understand your frustration and Daddy feeling bad! I feel like my DD has gone in and out of this phase constantly and she is almost 2!!

IMO - it's completely natural that your little one will respond to you more as you are with your DD 24/7 (almost!) and it felt like to me, that I was my DD's lifeline! I was her world - her moomoo! LOL!!
However, don't let that worry you because together DH & I have just been persistent and consistent in working together to reassure our DD that Daddy does actually know what he is doing!! We did let our DD cry when Daddy was doing things with her - I would take the moment to have a shower or make a cuppa just to give my mind a breather and my DH space to bond with his DD in their time and way.
If she got too upset DH would call and I would step in but eventually through DH being consistent in settling and playing, it felt like DD & DH began to sense each other and DD realised that Daddy was just as important as mummy and he too knew how the world worked!

This is just what worked for us and our DD - it could be completely different for us with no 2 (when the time comes!)
Something that we found really important for us but really hard in the beginning was staying calm and patient as we all tried to work each other out!

Make sure that you and your dp don't doubt your parenting and how great parents you are! It's just one of many learning phases that go with it!
I don't know if this is helpful to you at all - but am sending to you that it all works for you soon!