Gifts from a step mom to the bio mom

So we haven't had contact with my 4 year old step daughter in a year, obviously not our choice, her mother decided since he got me pregnant that meant he wasn't allowed to be a father. Well everything preventing contact between the two of them is no longer in effect but they're still going through family court because she refuses to follow any court order. We both talked and came up with the idea of getting her a mother's day gift this year because even though she's a cunt his daughter is still being taken care of and is still alive so she must be doing something right. She also has a 1 year old son but her sons father is a drug addict who isn't around so she literally has no one to do anything for her for Mothers Day. We are getting her a card, gift and inviting her, their daughter and her son to have dinner with us, our treat, but I don't even know how to go about signing the card or who's name to put on the gifts. She hates me and my husband and we know she probably won't show up but at least we offered to do something for her.