Have good checklist and procedures in place for transaction management, and use the same title company for both closings.

Richard Weeks nailed this one.

We agree with Richard Weeks , however there are do many variables involved.

The title company will make it all work.

You should have  the purchase contingent on the sale of her home - and use the same title company - Richard Weeks made great suggestions. 

Richard pretty much said it all.

Donna Flaherty Anything can happen. Make sure she is covered with a contingency on the new purchase and simultaneous closings.

I'd make sure the dates for financing are coordinated properly so that she is protected by her mortgage contingency clause if her buyer is denied financing....and make sure your daughter's exposure in the transaction she's buying is not greater than the deposit from the buyer of her home.... if she has not exposure in the deal and her transaction ends up a default, she will have a "wash"....

There is no best way. Every transaction is different.

And in each one there looms the FEAR of becoming homeless.

What you need, Donna, is extreme agility and oversight. Then always have a plan B. There is just too many players, whom you can not control, which could include a rogue inspector, who can sink the deal. Have a plan B that is an actual part of the strategy. That way, the buyer/seller does not perceive the event as the ship going down. Your life will be much more pleasant if you can intercept that drama and quiet the storm.