When someone is making contact, after a break, they sometimes want to do it very slowly and gently.
You do not say why the relationship has been so troubled, and it probably doesn't matter. What these cards are saying are that she doesn't want you entirely out of her life,but the fact that they only contain a name and nothing else, tells you that whatever hurt she felt from your troubles still remains and those cards acknowledge that, but still she doesn't want you actively in her life, hence the ignored texts.
I suggest you reply in kind. Send her a birthday card and Christmas card just saying something like 'love mum', do not be tempted to say anything else or put kisses on it and as she slowly escalates the contact (and I am sure she will), match her but do not exceed her.
I think you must think years rather than months, but if you are prepared to play the slow game, things could gradually come right, but do not push her, that will just make her retreat.