Not unreasonable at all.
I have no contact with my father or his side of my family. I find any contact from him/them very distressing. He does not know where I live but he sends cards every birthday and Christmas to my mother, addressed to me. I have thrown or given away perfectly good items he has sent as gifts because they remind me of him. He is a sinister presence in my life I do not want continually hanging over me.
I know at times my mum has felt conflicted about what to do regarding gifts and that I don't have a father I have a relationship with or how to handle this. What did she owe him and me? What was the nice thing to do?
At the end of the day it is not about being nice but the girls and I would be guided by their wishes regarding contact/gifts. Better to have an open and honest conversation with them and act on their wishes.
I prefer not to be told when things arrive for me as then he's not constantly reminding me he exists or making me feel that he can still get to me or is thinking of me. I don't want to think about him, or know I am in his twisted thoughts and that after all this time he is still trying to pull me back in so he can hurt me further. I don't want his gift or money, nor the hassle of trying to decide what to do about his actions, as I should not have to give him any mental energy. I should not have to be considering him at all. It sounds like your daughters feel the same way, but best to discuss it with them.
My mum has decided to keep the cards/gifts for if I ever want them but I have said I do not. I don't care what she does with them. I'd be cross if she were sending cards to or thanking people who have hurt me. She would essentially thanking them for upsetting me by continuing unwanted contact, all out of a misplaced sense of politeness or social duty. I love my mother and she is very caring, but she worries too much about doing the nice thing and that can actually end up being hurtful to her and others she loves, as some people do not deserve politeness or niceties. The usual social rules do not apply to them as they have already broken normal or healthy social contracts in appalling ways. I'd go as far as to say your ex's actions sound emotionally abusive, so I'm not all surprised by the reaction. I had the whole threatening to kill himself thing, too and I am just filled with dread by any sort of link or contact, even if it seems like a 'nice' thing. It's not to me due to the history, even sweet seeming cards feel evil as I know the motive behind is not loving but an desire to manipulate and harm. Might as well be a tarantula being sent in the mail, makes my skin crawl just thinking about it.
Put the girls first. Listen to them. They'll thank you when they are older. Don't worry about the ex and his family or doing right by them. They are a toxic presence in your lives who you owe nothing to.