Am I obligated to immediately forgive someone for a wrongdoing just because they are family?

Forgiveness goes at a different pace for everyone and is certainly not an obligation, but think of the severity of the situation. It always helps to be vocal and talk to the family member about what upset you, and how you can go about resolving the problem.

no. You have a right to feel every emotion you go through. You have a right to be angry, upset, and sad. You have been hurt and it takes time to get through that. You will get there when you are ready and only when you are ready.

You are not obligated to do as such. Your family may push that you should forgive them as soon as the wrongdoing is committed, but you are the master of you, and you do not have to forgive them ASAP. Handle your emotions first. My family always pushed us to forgive each other immediately, but that does not have to be the case. You are your own person. Take your time, but let them know how you feel.

No, you aren't. Forgiveness is something that has to be earned or in some cases, you can never earn forgiveness. Just because they are family doesn't mean that you have to immediately forgive them especially when they don't admit or know their wrongdoing. But since society pushes people to forgive others easily, it has made an impact on forgiveness. And even if you do forgive them, you won't forget it. So my recommendation is not to forgive them now but when you are ready to forgive them since their wrongdoing might've caused some emotional stress or lowering your self-esteem.

Certainly not. Forgiveness is a meaningless concept unless it's earned. The only way to properly earn someone's forgiveness is to make sure that your actions consistently align with the promise you've made to improve your behavior. If there is no change in one's behavior, then thr person who wronged you cannot rightly claim that you have an obligation to forgive them. This applies to all people equally, so it doesn't suddenly stop being valid just because you're dealing with family members. Now, family members may try to guilt you by playing the "oh, but we're family" card. In such cases, I think the best thing to do is to internalize the fact that they are indeed trying to guilt you, and not accept any unearned guilt on your part. If you think they'll hear you out, you may even bring it to their attention.

It depends on which wrongdoing was done. If it is something which stems from our inherent imperfection (for example, they told you something, which hurt your feeling but what they said in itself wasn't derogatory or abusive and it was solely because they didn't fully understood your situation) you can forgive them but you needn't to do it immediatelly. If there was something hurtful done in order for getting some other benefit to you (for example, a medical procedure in formal healthcare system (not by a charlatan), you can forgive them. Sometimes some sacrifice is needed for greater good. The same is true if you for example had to endure work stress (which is solely related to work - tight shedules, large workload or overtime for example) in order to get salary. If there was a serious abuse which has no excuse (sexual abuse as worst case of abuse) it is obvious that you can't forgive them. Then you needn't forgive them. You have to report them to authorities, not forgive.