Hi Gimlimike
I can not talk for the 31 but would think that this would fit your needs and depending on the age of the grand children as to there sleeping area requirement, I can sleep upside down like a fruit bat so room is not a problem for me. As for tiller or wheel, personally I would not be without a wheel though it can be a pain when boarding (fold up optional). I like to steer with my feet on lazy layed back afternoons and going out through the bar its great to hold on too, there are many other advantages (for me) having a wheel.
The shallow draft option is good with access to tight spots and anchoring close to shore especially with the little ones and on a lake, perfect.
Have you looked at many boat to date or is it early days in your search...?
I hope others with similar size yachts add to this thread with how there boat size works for there families
Having a 36 ft is perfect for my wife and I and anything smaller would not be suitable as we can have our own space, however we all have different needs and it is important to make sure that you find the right size boat that will work in well with you and your family, in ending, will there always be 4 adults and 2 children on board most times you sail and would you sail most weekends...?
Regards Benjamin