My mother and step father were able to obtain temporary guardianship of my daughter(8) under false alligations. We have a hearing scheduled this week. I have had to move and make serious changes in my life for finances etc... if they lose the case in their efforts to take and keep my child from me, can I sue them for emotional distress? And for financial burden?

Probably yes... but you have to show clear and convince evidence that their behavior was malicious.It is your burden...

However, you can certainly sue for court costs and attorney fees to fight them.

My mother and step father were able to obtain temporary guardianship of my daughter(8) under false alligations. We have a hearing scheduled this week. I have had to move and make serious changes in my life for finances ect...if they lose the case in their efforts to take and keep my child from me, can I sue them for emotional distress? And for finacial burden?

I think you're jumping the gun here. You're asking about suing for emotional damages after winning a case that you haven't even won yet.

Out of curiosity, what allegations did they make against you? It is not uncommon for people to lie about one another during custody battles - the difference is being able to prove it. What did they prove about you that led the court to believe that your daughter would be better off being placed with them instead of you?