Rosetta Stone,
As others have said, only you can judge your personal contrition. However, you can receive guidance in doing that, which I will try to do now. As Benedict108 said, consult above all with a good and faithful priests over this, above the advice you receive here.
Let me start with this advice, which I have found so many people need to hear. If you do not, I apologize.

The resolution not to commit a sin again does not mean you will, in fact, never commit the sin again. You are human, and however strongly you resolve, you may again fall. In fact, a person may even leave the confessional with a very firm resolution not to commit a sin again, and then minutes later begin waffling on that intent, or even begin to say to himself, “I want to do this thing.” That’s the nature of being a fallen human being. Now certainly, this is no excuse for things to remain this way. Fallen human nature as it is, with prayer, pennance, personal sacrifice, and general growth in holiness, a person can overcome this nature so as that he or she will not begin to waffle after leaving the confessional.
Nevertheless, what matters is what your intent and resolution was as you made your confession. When you confessed your sins, and when you made your act of contrition, did you do so with the clear intent in your mind that you did not really mean to turn from the sin and that you were not going to invite your father the next time? If so, then you were not absolved of that sin (it being, in all likihood, venial, as has been discussed, it did not impact the rest of your confession). However, here are some other possibilities as you made your confession:
- You resolved - even grudgingly - to invite your father the next time, but felt that when the time came you would not be able to gather the strength to do it.
The sin would be absolved. Your own fear, while not helpful in completing your resolution, is another issue from the resolution itself.
- You resolved - even grudgingly - to invite your father the next time, but felt that when the time came you would not be able to gather the strength to do it and you had the feeling of hope that you wouldn’t, but you - even grudgingly - “said no” to that hope and intended to invite him.
The sin would be absolved, so long as that last “but” was in there. As long as you made a decision against that hope that you
felt, you were good to go. Remember, choices count; feelings do not.
There are other possibilities, but hopefully this gets the idea across?

Only you can really tell what you felt; you just have to make sure you are really judging the right thing, rather than some of the other side things I’ve mentioned.
Also, a few other points that I think are important. This was, it seems, almost certainly a venial sin. Now you said you
have invited him since, and so you, in actuality, have repented of it, regardless of what you did at the time of the confession. The reality is that you’ve been forgiven this already… Venial sins are forgiven in any number of ways when they are repented of, such as reception of the Eucharist and by making the Sign of the Cross with Holy Water, and perhaps most importantly simply by going to confession - even if you don’t specifically mention it - after you’ve repented of it.
As such, I’d take all of this advice to judge your confessions about more serious sin in the future (supposing that you have these, and hoping that you do not), but not worry about this particular sin. You’ve invited your father, so you’ve repented of it - even if your feelings are still not fuzzy about having invited him. In fact, if you don’t feel fuzzy but did it anyways, then your repentance is in a sense even more meritorious than had you begun to actually feel happy about inviting him, as you have made a
choice in favor of doing what is right in spite of unpleasent feelings about it.
Of course, working out the vice of those negative feelings is still something to work on, if indeed they can be worked out.
God bless