That is normal. Many people question whether or not they can go on in life after a loved one is gone. It takes a long time to fully process the death of a loved one and start living again. You will always remember them, even if you don't think so. Those memories of the lives you shared will not go away. And later on you may smile when thinking about them instead of crying.
Not attending a funeral is OK too. I always recommend it as it provides some form of closure, however, some people are not ready to let go. Being strong enough has nothing to do with it, you are not 'weak' because you did not go to his funeral. You were mourning his life in your own way. That is appropriate.
If you feel like you are able to attend your dad's funeral I would. Like I said it may give you some closure. This does not mean that the pain and grief will go away, but that you may be more ready to accept and deal with it at an earlier time. Being present both physically and emotionally at a funeral can help the healing process. It can be very difficult, but down the road you may thank yourself for going.
Whatever you choose try not to beat yourself up over it. They were special people to you and both of you knew it. The outside world will never know how much they meant to you. And you don't have to prove it to others either.
