Can you wear her? Just put her on your back in a carrier (Ergo, Pikkolo, etc) and continue doing what you have to do while talking to her, doing stuff with your older child, even going to the bathroom.
What about if you take one day to just do stuff with the kids? Leave the housework, errands and appointments for another day. Just sit on the floor with them, play with them, tickle them, curl up on the couch and read books, take a nap, make their favorite foods for lunch.
I am really sorry that you are dealing with the stress of a cross-country move, the loss of your mom and a crazy toddler...it must be so hard. I hope that things get easier soon.