It is very typical for a child to prefer one parent over another, even up to three-four years old. It is also very hard on both parents. The one who is preferred because it is physically and emotionally draining to be the one to do everything, and the one who gets neglected because, well they feel neglected and can't do anything to help.
The key to this is patience. You are right in saying it is just a phase, it can be short lived or a really long phase. I have studied Child Development and also have personal experience in this area. So here is my advice... and I hope it helps you.
My second daughter (Ella) was like this, she is now 6 and when she is feeling insecure she still only wants me to do things for her. But will reluctantly let Dad help. We have worked so hard on this, for the same reason you want to, my husband was feeling so left out.
My first child did this too, but not quite to the extent of the second. Now my two younger ones watch how I treat him and how the older ones treat him and they all enjoy him now.
The first thing that I did was make it REALLY exciting when Daddy came home form work. Lots of hugs from me and anticipation leading up to that point. "Daddy is coming home soon:)" "When Daddy comes home, lets give him a...." and find something that we could do for him.
We also spent time during the day making secret things for him, like pictures or cards or love notes, and would put them on his pillow. or make treats to give to him. Which in turn I asked him to make a big deal about! And do the same things for her.
He came up with a "running hug" (back up as far as she could and run run run and jump into his arms) because it was one way she would actually hug him. He would try to hug her or ask for a hug and she would decline, but if he said,"can you give me a running hug?" she would be running and hugging within seconds.
We started alternating who would put her to bed. This was really hard for her at first and was actually more helpful if I went shopping at bed time, on his nights. Every other night we would trade. And it got easier. He actually did a different more fun routine then I did, and now she likes him to put her to bed more then me!:) (most nights) But we still take turns because we have 4 kids and they all want us to rotate.
Another thing we do is daddy dates. They absolutely love this. My first daughter is 8 years old, we started this when she was about two to give me a break. She would just go run errands with him and he would make sure to do something fun like, stop by a park for ten min, or get a little treat or something. So now they all take turns, I mark it on the calender whenever he takes one and then the next time it is the others turn and on down the line. This has really helped the bonding and they love to ride in his truck and spend time with him.
We have also done non-giving-in in situations where if I am busy, Ella could have Daddy do it or wait till I was done, (which I can always look busy even if I am not). You can tell them that they can do it or Daddy can do it. This helps encourage autonomy too. These are hard at first with lots of tears, but once she realized that I wasn't going to help her, it got easier.
It is great for you to have a night out weekly. they will like Dad more when he spends more time with them. So if you were to make their time more frequent, it would only help them get closer and for them to trust their daddy more.
I think most important is, once you decide what kind of things Dad is going to do, you don't give in. It may take a while but if you stay consistent and positive, they will come around. It is a hard situation, but they will come though with lots of encouragement and support from you and unconditional love from dad.
Good Luck
E.