You need to sit down with a solicitor (not an estate agent) and walk through this process.
Your biggest problem is the negative equity/tracker mover mortgage and the 28 day time limit.
Probably the best thing to do is to put your own property on the market and see if you can find a purchaser who is willing to hang around, to close, until you are ready to move out. Most purchasers take the view that if you want to sell, and you want money from them, you need to move out. They are not interested in your circumstances.
More likely, you'll get a good feeling about the chances of your place selling when you are ready.
"Some have also stated that we couldn't sign contracts on our new property until we are sale agreed on our current property, is this correct?"
Your problem is being tied in to a contract to buy when your own sale has not closed - what happens if your purchaser can't get funding?
The best advice always is to sell first, bank the money ( if any) and move home to mammy or sleep on your best friends sofa.
Your circumstances are such that you will need a great deal of luck and a very patient, solvent purchaser to wait on you while you try and tie in two, un-related transactions. Many people in your circumstances take the view that both transactions are related - and yes, they are, but only to them - not to their purchaser or their vendor.
mf