your parent that is in the US should be able to adjust status but should not leave for any reason until green card in hand, otherwise they will be barred from the US for 10 years. they should not apply for advance parole as they will not be able to travel anyway.
If the overstay is the only problem then you should be able to do the forms without an attorney, as Parents of US citizens are forgiven for overstay when applying for green card. If you search this forum there is a LOT of information and advice about the process.