Very unlikely, legal aid has been drastically cut in the last few years.
Legal aid is only available in domestic situations such as this if there is a danger to the children, due to violence , threat of abduction or similar.
If she has already run up the bill I think it is too late anyway, you have to apply for legal aid and your claim accepted before you start proceedings.
How has the 'large legal bill' been run up? (to see if it could be one of the few things that aid may be available for)