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I have to agree with your psychologist that mistakes were made on both sides.
But for family harmony, somebody has to make the first move, and your husband has asked you to do it. Rather than an apology, since you don't think you did anything wrong, maybe you could just offer an explanation that you have been having postpartum depression and have felt very overwhelmed at times.
It does seem that it would be best to be friendly, but not actual friends with them. See them at gatherings, and swap the occasional favor with them, but don't confide in them or discuss details of your marriage. Just brag on the baby and keep things light.
This is another one of those situations where you end up having to choose whether it's more important to be right or to be happy. If giving them an explanation and just going on in a friendly, very casual way will help bring the family back together, it's most likely worth doing. Yes, even though they didn't react in a kindly way in the past. You'll want your son to be able to play with his cousins as he gets older, and for you all to have happy holidays, (so you don't end up home alone on Christmas Eve, etc.) so it's worth swallowing some of your pride. Your husband will appreciate that you made the effort, I'm sure.
Things are very rarely fair and even in family dynamics. It's just one of those unpleasant facts of grown-up life.
I hope this makes sense to you. It's not that I don't understand that they were mean to you at times...it's just that you're in this family for the duration, and sometimes we have to go along to get along.