Its a little more sticky but very do-able in summer. DD1 co-slept from birth - 6 months and she was born 22nd october so she co-slept right through summer. We are now co-sleeping with DD2 and lastnight I did the same as you, short sleeved suit, muslin and a light blanket (shes sleeps on top of our blanket). Try and find some 100% cotton suits (short sleeved) for her to sleep in. Muslim wraps are great because they are breathable and 100% cotton.

You can sort of "wean" her off being wrapped. She will get used to it and her hands will stop waking her up.

Just nod and agree with your mum, I do that with mine. Ofcourse they always know better....

Do you have a pedestal fan on in the room to keep the air moving around? Lucky it doesnt usually stay too hot for many months in melbourne.