I have the same situation...sort of. Whilst my family are supportive of me if I actually start showing results (not just weight loss, but anything) then they support me..its just the first initial period because i'm a very whimsical person and rarely stick to anything. Plus I always feel like I'm being constantly compared to my brother - we both have a lot of achievements in different areas, but I'm the "screw-up sibling" as my friend puts it.
It was a long road, but I finally learnt that a group of supportive friends can more than make up for a lack of supportive family. As the adage goes, you can choose your friends but you can't choose your family. To that extant, as much as it hurts, reserve your victories for yourself and the people who won't put you down. You do not need such negativity when you're losing weight: its already stressful and emotional. Plus also, all it is, is jealousy on your mum's part. My nan always says 'Jealousy is a fools game', nobody benefits from it, so try to ignore it - though I understand how incredibly hard this is.