I'm so sorry for your loss op. You have a lot of pressures you are handling so make sure you ring fence some time for yourself on a weekly basis, even if it's just an hour or two.
Agree with pps that your middle child may be severely anxious and it manifests itself in talking constantly and wanting your attention and reassurance?
Another possibility, although this could be completely wrong , is have you considered that your DD may be autistic? Perhaps talk to her school. Being "broadcast to" or "spoken at" can be a sign of asd.
If the above doesn't seem likely then try the following techniques:
¶ When you are busy and don't have time to talk to her, quickly stop what you are doing, turn around, look at her, and and hug her, or place your hands on her head or shoulders, or her arm , in a comforting way, and let them rest there for a long moment. So you are replacing talk with a brief intentional physical touch until you can get to the point when you can speak to her to properly. This technique is usually used for younger DC but you never know, it might work!
¶¶ Perhaps ask the eldest to baby sit the youngest, take your middle dd out for a coffee alone and really focus on her and say you have noticed that she wants to talk a lot and ask her gently "what do you need from me?" and then fall silent and see what she says?
¶¶¶You could then try and ring fence one hour one-on-one time with her on a weekly basis outside of the house and then you can get to the point where you say "I am sorry, I am busy doing X right now, could we please talk about it properly during our "special hour"?"
¶¶¶¶Another technique is to ask her to write the subject down on a square of paper which she "posts" in to a jar, and then you take the jar out to prompt you to discuss the subjects at "special hour".
¶¶¶¶¶ At home, at the table, when discussions get heated or everyone is talking over everyone else, you could try the wooden spoon (or carrot) method. Whoever is holding the spoon or carrot , gets to speak for 3 mins and everyone listens and then you pass on the spoon or carrot to the next person to reply. Maybe try that at the table regularly and get your eldest on side first, and eventually the lesson sinks in.
Good luck!