l need an advice

l came to the uk in 2012 to do masters and thereafter my phd in 2014. l brought my wife along with me in 2014.she works as a health care assistant.unfortunately, my visa was curtailed in 2015 and we were told to go home by Dec 1 2015 but due to the fact that my wife had complications in her delivery and she gave birth on the 18th of DEC 2015, we couldn't go back home.so we stayed back so that she can receive proper medical condition as advised by the doctor but we didn't inform the home office due to the stress the delivery brought on us. on the 27th of October 2016, we received a letter from home saying that we should bring our daughter home for FGM because my wife was circumcised when she was a little girl and there are doctor's report to confirm it.we sought for advice and we were advised to apply for discretionary leave to remain. which we have done. my questions are as follows: what are the changes that our application will be granted, how long those it take for the home office to respond because we applied on the 1st of December 2016 and they have taken the money from the account. thanks in anticipation of your response.cheers.

It can take a few months, you will just have to wait.

How have you been supporting yourselves financially?

If you had no valid visa after 1st December 2015, I hope that you have paid ALL the NHS fees in relation to the birth and subsequent NHS use as with no valid visa, you and family have no entitlement to use NHS for free.

You should be prepared for a long wait. Applications submitted under Discretionary Leave generally take some time for a decision to be made.

To be honest, the Home Office make take the view that you could settle back in your home country away from others in the family who are pressing for your daughter to undergo FGM.

Some points to consider:
If you have no current leave and under your stated circumstances you have applied for DL it will be a refusal. Prepare yourself for that outcome.
The perceived threat of FGM will not give you a strong case to prevent return. There are a number of other options including relocation in your home country.
The letters from your family will be treated as self serving, so don't expect them to be believed.
Is FGM specifically illegal in your home country? If yes then this further weakens your case as you are afforded state protection in preventing the action.

While I totally support any action to prevent FGM and prosecution of those that perform the action, you will have to prevent a far better case than you have outlined.