Firstly, I must say that I take my hat off to you, taking care of a 1 year old, and a nearly 3 year old, 5 days a week! I've recently taken care of my 1 year old GD, on a couple of occasions, for 2-3 weeks, to help out with childcare, and I've been absolutely exhausted! She's very well behaved, but she's on the go non stop, and I no longer have the energy that I had when my kids were little!Lol
Obviously, your 1 year old GD really doesn't know how to misbehave and she's just copying her older sister, and as you say, the 3 year old is simply craving attention, as she's not getting any from her mother. I think the key is to try to keep them both occupied with fun activities that they like to do, or things that are new to them. Probably a little more difficult with a 1 year old as they're not really old enough to concentrate on anything for long. But if you can get the 3 year old engaged in something she likes to do, and you share it with her ... a big colouring book with lots of crayons, or one of those wipe clean floor mats, play-doh, lego, those little felt boards, making cakes with her (sit the younger one in a high chair in the kitchen to watch, and give her some cake mix to play with!). The key is to keep the older one occupied, because once boredom sets in (and we all know how easily kids get bored!), that's when she may display unacceptable behaviour.
Hopefully, overtime, your older grandchild will see that time spent at grandma's house is enjoyable, and she'll feel loved and wanted, unlike being with her mother who sadly sounds like her children are a bit of an inconvenience.
I agree with what some others have said, that your older GD certainly sounds like she's ready to go to nursery, and you'll probably find that with more structured play, and lots of different daily activities, her behaviour will hopefully improve. And this will give you more time to spend with the 1 year old, and hopefully her behaviour won't deteriorate like her sister's, as she'll be getting plenty of one-on-one time with you.