I think your best bet would be to take a private tour. We did this with two elderly people who could not walk very well. We paid more but it was well worth it. They take you on the regular tour plus up by the west and east bluff to see the houses and views. Great pictures of the Island. I thought we talked to the regular carriage tour and they set this up for us. I would call the Mackinac Island Tourism Bureau (800) 454-5227 to find out for sure.
Reba's rents electric wheel chairs for the day. If you are bringing bikes you could ride around the Island. It is flat all the way around. You can walk, but bring good walking shoes.
The butterfly house would be good for rainy days.
It also depends on how old your kids are.
There are three parks with playgrounds. One by the school(which my 5yr. & 9yr. like the best because it is by the lake.), one in front of the fort, and one at Turtle Park in the interior of the Island. Turtle park is by the cemetaries. They have a soccer field, baseball diamond, and horse arena. The playground has picnic tables with charcoal grills and a bathroom. It is hidden by the trees so you have to walk down a path to get there.
Go to www.arnoldline.com to get a coupon. Buy two adult tickets get a free childs ticket(5-12yrs.) or get $10.00 off third adult. Children 13yrs. and older are $21.00. Children 5-12yrs. are $10.50 and under 5yrs. are free.
Here is a package that includes a carriage ride, the butterfly conservatory, the Fort, tour the Grand Hotel and your choice of Ferry line round trip ticket. You also get a $10.00 voucher for the Grand Hotels luncheon buffet. Adults are $59.00(18+), youth are $55.75(13-17), and children are $28.25(5-12).
There is a putting coarse by Mission Point. It was $5.00 for children and $10.00 for adults. Well most of this is to do when it is not raining. Hope this helps.