Agree with Mikey. Have been a couple of times and it is really just another Isle of Wight with shops. Once you have had a Singapore Sling at the Raffles, bought a load of stuff you don't need and had a few interesting meals that's about it. (And don't forget your son and d-I-l will probably have to be at work for most of the time.)
And it is hot! You will find it quite exhausting. Obviously the shops, hotels etc are air-conditioned, but you have to go out sometime. Traffic is mad, so it takes ages to go anywhere in a taxi. Please rethink both the Singapore part of the trip and Australian part, (two months is an awfully long time to be a guest in someone else's house, no matter how kind and inviting they are.)
Possibly spent one week in Singapore at the beginning, to get over jet lag and get your bearings, then two weeks in Australia with your friends, a week in another part of the country on your own, (small hotels don't have to be too expensive and you can take the train or bus to get around. Perhaps ask your family to treat you to this part of the holiday?), back to your friends for a week, this will have given them a break, and finally back to Singapore for a week.
I understand that you have been saving for a long time and want a special holiday, but as a 60+ traveller myself I think you will be bored to death going for such a long time.
Any money saved can be used for quick trips to Europe. Good luck and think hard about this.