YANBU to want or have the wedding that suits you best.
I would want my son to have the wedding that he wanted when he is older. But if the wedding that he wants is a wedding that I am not invited to and only find out about after the fact, I would still be very hurt and upset.
However you dress it up, and whatever reasons you have, you still did not want them at your wedding. Your parents can deal with that, your DH's clearly can't and you at least have to try and understand that they have the right to feel upset about it. It doesn't mean that they are making your wedding all about them. It's a bit like breaking up with someone and saying "it's not you, it's me" to make them feel better. It never works.
You know your reasons and have clearly thought about them long and hard. Your in-laws seem to have been taken by surprise by them and are feeling rejected and confused by it all.
I'm not having a go OP. I have a MIL who cries for days and cannot sleep too (very long story) and for this you have my sympathies.
But you can't have it both ways. On the one hand you are saying that you have been together for 13 years, have two children, it's a second wedding for your DH, you got married for practical reasons and you wanted a low key affair with no fuss.
And then you complain that you haven't been contacted (other than a card with money in it), haven't been congratulated, haven't been welcomed into the family you have already been a part of for 13 years and that you feel they are spoiling the newlywedded feeling of it all by being upset.
I think that if you chose to have the sort of wedding you did, and are happy with your choice, then you can't complain later about a lack of congratulations from the people you kept in the dark. You can complain about the guilt trips, and if they had rung you on your birthday to tell you what they thought of you they would have been badly in the wrong and making the situation much, much worse.
They are in the wrong to pile on the guilt, but you are in the wrong to compare their reaction to that of your parents and to take offence that they haven't congratulated you or expressed their disappointment in a way that suits you best.
I'd just leave it now. If you are not speaking to them (in whatever sense) then your DH needs to say to them, for one last time, that none of this was done with the intention of hurting them but now it is done and it's not helping anyone to go over and over it. You all need to move on. Then stop worrying about who should have contacted who and who ignored what email and just behave like you always have, talk to them normally and hope they can do the same back. If not, it's down to them to either forgive and forget for any perceived slight or bear a grudge and split the family.