Please be cautious if you are commiting something to writing to give to your mum. I would suggest that a few visits with the kids that are short and sweet might help re-build the bridge slowly. It just takes time. From observation I've noticed that essentially our families and 'friends' are basically just frightened. Frightened that we've left, frightened of what that means, frightened of what we might say to them. When seeing extended family that I don't keep in regular touch with I always take the lead in establishing how our relationship will work. I always greet them with hugs and kisses, before they even have time to think. Once you've managed to get a hug in, their defenses are down and you can continue to direct the way your meetings together will work. Suddenly their fear is slightly abated, and by including them in my life by sharing funny stories and staying clear of any difficult topics, by the end of the visit they are much more comfortable and will respond even more positively next time. The elephant in the room becomes smaller and smaller over time until it just isn't there, or if it is - too small to notice.
When it comes to my mum, I now include her in all aspects of my life. Initially after leaving the borg I kept most of my life secret, but over time I've tested the water by including more and more challenging things. My mum openly states that she is happy with the way my brother and I have turned out (brother is out too) - we've managed to demonstrate through our actions that we are not frightening people, we don't say frightening things and we love her dearly. Mum now knows that she has nothing to fear. I live with my partner and we are not married, and my mum adores him. She has even bought us bedroom linen and often refers to my partner for help with things in her life. She has learnt that even though there are differences, we are still family and my brother and I are good and loving people.
On the birthday front I have no advice because I don't have children. One thing I do though is call mum every year on my birthday, sing her happy birthday and make a big deal about how happy I am that she gave birth to me and that it is a day to celebrate our lives together. Now when there is any mention of my brother or I having birthday celebrations she doesn't even blink. In fact now she calls us on our birthdays and says a very sweet happy birthday (no singing though - which is probably for the best, I love her to death but she can't sing).
Though I don't agree with the WT - I don't actually want to damage my mother's faith, so it is not in anyone's best interest to get into the details and problems. If mum were to lose her faith she would be devestated and no doubt incredibly upset that she has wasted all of her life believing in lies. I'd rather see her happy and maintain her faith which she relies on to get her through the tough times. I openly refer to her faith but always in a positive way, if she is down or struggling I suggest she pray and remind her of passages in the bible from which she can take strength. In this way she has also come to feel confident in sharing aspects of her life openly with me. It's a long difficult journey, but I think I am closer to my mother because I am not in the borg. I think she knows that too - and that is really the elephant in the room. It's an elephant I'm fond of.