It might seem counterintuitive, but how your readers will feel about the events in your story, including a certain character's death, shouldn't be your concern. You want readers to feel sad over this death, and you're trying to bend the story/characters around that. That's manipulation and contrivance. You're approaching this backwards. Just tell your story as it happens.
Your readers will decide how to feel about the death, and readers, just like customers, are always right. Your job is to portray the mother as she is, and you already know how she is -- loud, gossipy, wacky, sometimes serious. Obviously she is very clear in your mind. Don't sell her out.
Mostly your readers will take their cues about how to feel from your main character, regardless of the mother's personality. Everyone loves their mom, of course, even if they are annoying harpies. Don't try to write a "sad" situation. Just write what happens, and it will either be sad or something else. "Something else" isn't necessarily a bad thing.
As for your funny robot idea: It is funny. (But, I wonder, what makes a robot male or female? Maybe that's what's funny about it.) I don't think the idea of a "trans-gendered" robot is automatically inappropriate for kids, unless you start cracking a lot of Will and Grace-style gay jokes. But would your main character take heart-felt "motherly" advice from the family robot? That's for you to decide.
Btw, just typing "family robot" made me laugh, so it's obviously funny.
