Make home made play dough - there are lots of recipes on line and play with it
Finger paintings - with real finger paints or pudding
Buy a few toys that are grandma house toys.
Any kind of simple baking or cooking project - making a sandwich can feel like a big accomplishment to a toddler.
Make home made musical instruments and have a parade. Rice in a bottle you seal closed with duct tape can be tons of fun. A drum made out of an oatmeal box or a meal mixing bowl. A horn made out of a paper towel roll.
Make an personal alphabet book. If you mom has a digital camara. Take pictures of a favorite thing for each letter and paste them into any kind of blank book, even a black and white composition book to make his very own book. Your nephew can help find things that being with the letter if he knows any of them.
simple obstical course - a tunnel under some chairs, walking around some other chairs, crawl over some pillows, anything like that.
Make a tent and have a tea party inside. My DS loved this game about that age. But it can be a bit tough on grandma to get inside the tent.
Get bath tints for bath time and show DN how two colors mix to make another one.
Do you have any of those indoor play gyms (my gym, jungle of fun, party gym) that have open playtime nearby? For around $5, you can play for as long as you like and its a great way to tire Nic out (he's 20 months, but we've been going for a while)
We also walk the mall... ride the carousel, throw pennies in the fountain. One lap around the mall (no shopping, strictly walking outside the stores... I tried to run in and buy something quick once and it was a disaster) and Nic's pretty tired...
Also, I bought a $3.00 tin of 50 plastic cookie cutters -- they are letters, numbers, and holiday shapes and they come in 5 different colors. These things are priceless (but i think most of them would suck as cookie cutters). I bought a different tub to store them in since they came in a flimsy one... we take them out of the tin, identify what they are ... sort them by color, sort them from letters/numbers/shapes... right now, he's really into handing me one to identify (thats a blue M for Mama) ... seriously kills about 3 20 minute sessions a day...
On nice days, we'll take a walk down the street... but, I miss when parks were doable...
Blocks are also great... and when we go to grandma's, she has "blocks" made out of all sorts of food boxes ... oatmeal containers, parmesan cheese round ones, empty spice jars and everything in between.... all sorts of shapes/sizes from huge to tiny ... he LOVES playing with them....stacking/sorting/knocking down...
What about playing with kitchen stuff? My DD loves to play with the tupperware containers, stack them inside each other, find the matching lids etc. She also likes to play with large plastic bowls and wooden spoons and "mix" up things for me.
What about books? My DD is a bookworm and could spend half the day reading and being read to. If she doesn't have baby books magazines work as well. Especially ones like National Geographic with lots of animal pictures.
Check to see if there is a mall nearby that has a kiddie playground. My local mall has a one with a few climbing structures, and it's free. There are usually lots of moms there with toddlers, and my DD is exhausted after less than an hour of playing.
whenever my friends go away and leave teh grandma with the toddler, I always make sure to stop by a few times. Can the leave a list of friends who have kids, and maybe your mom can set up play dates.
My son loves to play "ball ball" we kick the ball back and forth to each other. I make sure I don't kick it directly to him, making him have to run for it! LOL (i am so tricky, I can outsmart a 23 month old! LOL)
Depending on how your sister feels, you Mom could take the baby outside and play. I see you live in BC, so I am sure it is cold. But we take out son out even when it is 30 outside. Granted, not for too long 20 minutes or so, but I thin kthe fresh air helps!
Also, bathtime is a good "relaxation" baby is confined to one place, and usually loves the water!
You sister should also buy some new books. We are planning a cross country flight, and I bought my son a bunch of the little people books... they have lots of flaps, he LOVEs them (we have one we read right now, the ZOO book... he has loved it for the last 4 months or so).
I think a lot depends on how well your mom gets around. My in-laws are still young and FIT, so they could handle my son for a week. My parents on the other hand... NO WAY. So I really think a lot depends on what your mom is comfortable with.
The weather here isn't too bad- it's rainy season, but still mild in temps. My mom is somewhat active, and can definitely get down to play with him and take him to parks, but not as much as my sister does. (She takes him out running- he loves the wind in his face)
One thing I know I loved doing with my mom (when she had a day off) was having a picnic. We would make "special" sandwiches (cheese, sausage and crackers) and eat them either on a blanket in the front room or on the front lawn. It was just fun to pretend.