Update : Just to let you know - I have asked some of my personl contacts and family members about your mother - If I do hear of any info I will let you know - I do know that by doing my research - I have come across alot of Alice Inkpen's in the family history - and one of them is possibly your grandmother (if your mother named you after her- which in most cases - it does happen this way).
Have you tried Nova Scotia Archives to search for Alice Inkpen - you may find more info - but I do know that there are a lot of Alice's in the history of Inkpen names - I just checked it this morning - and WOW - lots of Alices - just have to figure which one would be born around Nova Scotia area - or that was born around 1957 - that maybe had the middle name as Alice - or you can request vital info from the NS Vital Stats Dept. on Inkpen's born in and around 1957 in the province. this government should be located in the Halifax area.
I hope you find something more - and if you need my help - I am happy to assist you - as if it wasn't for this site - and ancestry.com - I would have never found my half sister and brother! Take care Ivy