Hello @johncottingham - What a great question! The statistics on decreasing muscle tone in people as they age are alarming, and definitely contribute to falls and injuries, so it is great that you want to take action. Also, when your muscles are weaker, your balance can be affected, and even a short illness or hospital stay can make you weak enough to make recovery and rehab too difficult.

The first step is to check with your primary care provider, to ask if there are any exercises you should avoid due to your own physical conditions. Then, you can check with your insurance company to see if you are eligible for a local "Silver Sneakers" program, where all participants are of Medicare age, and programs are designed to accommodate some of the conditions that come with aging. Some communities also offer dedicated programs.

If you want to pursue a home program the two of you can do together, you can take a look at these examples.
Be sure your balance is as good as possible first:

Then begin some basic strengthening exercises that don't require a gym or special equipment:
https://www.silversneakers.com/blog/strength-training-for-seniors/
And basic Chair Yoga (this is a lot more challenging than it sounds):

Finally, if you want to do some (light) weight training:
https://www.livestrong.com/article/110562-dumbbell-exercises-seniors/
Do any of these ideas give you a place to start? I'll be very interested to hear what you choose to try.
Sue