First of all - doesn't your contract spell out the time frames for all of this?
Apparently not, or you wouldn't be asking......
next question I have is.....do you have an agent (who would be the right person to ask )...........apparently not, or you wouldn't be asking strangers on trulia!
So.........you accepted an offer subject to the sale of another home (I'd ask you WHY?).......did you put a set period of time for that to take place? How long do they have to get their home "sold".
And.............by "sold", do you mean "under contract" with an offer in place and contingencies met..............or closed??
How long do they have to obtain a mortgage commitment?
Lots of questions here..........answers are needed in order to really answer your question.
In my opinion, as a listing agent, I would expect the buyer's mortgage process to move along at the same time as the other contingency (the home sale).
In other words, I see no reason why they shouldn't process their mortgage application in the normal manner, and not put it on hold until their home is sold - that includes having the appraisal done.........why wait for weeks for their home to sell if there is a chance the house won't appraise out or they might be turned down for their loan?
Are they following through with the home inspection, or is everything on hold until their house sells?
No idea who advised you , but it wouldn't have been my advice.
I see these two contingencies as parallel but separate. Their mortgage commitment will most likely be subject to their home selling, but at least you'll know they are approved and the house appraised out.