Onthedowns sorry they have been so rude to leave you out and then to chase a birthday message.
Could this be a way of trying to make amends (funny old way but still).
Please do whatever makes you happy.
It's not your dh's call to make.
She has put the ball in your court "she replied saying anytime after 11 April."
So you could just leave it and see if she chases you up (least confrontational way to do it) and ....
if she does not, then when you meet and she says you never got back to me just smile and say 'oh well, I'm here now.
or
If she chases you, you decide what to do, do you want to meet, if yes, meet, if no, then don't. In which case you can either just keep saying 'I am a bit busy at the moment' or be honest and say 'I feel like was me making the effort a lot over the last few years, I felt left out and excluded and now have realised I don't actually feel the need to be included any more. Plus I am very offended you chased me for a birthday greeting having ignored the fact I had a premature baby!"
But (because I also don't like confrontation) I would also say, something like - "...any way that's all water under the bridge, let's just leave it, we will meet up at weddings and the like and that is fine."
In your shoes I would not fish around for an apology or even an acknowledgement of the wrong done to you.
You know it, and this so-called-friend chooses to reply and say sorry, take it from there.
But she may well not choose to apologise and may feel you are getting at her, at which point you would need to simply say "...my hands are full with a new baby and after many years of no contact from you and other friends I've realised who my friends are, people who are involved in my life....." or words to that affect.
Good luck.