My name is ***** ***** I have been a solicitor for more than 30 years.
You cannot report the chidlren as missing as you know that they are with their mother - and indeed you have a good idea about where they are.
In fact whilst the police will visit and check that they are OK they will NOT tell you where they are - only that they are "safe and well"
You need to be very careful about how often you drive past the godmother's house - and you must not call her again as there is a very real risk that she will report it as harassment
Realistically it appear that your wife has left you - which does NOT mean that your relationship with your children should be put on hold.
One way forward is to make an immediate referral to Family mediation using the gOdmother's address for your wife
In addition if and when you decide to apply to the court the form you need is a C1 available here
Please ask if you need further details