Advice on gaining the trust of my girlfriends mum?

im 16 and been going out with my girlfriend for 2 months now. and she stays at mine til late on a saturday and i suggested maybe her staying over.would be nice just to cuddle up and spend the night with her but her mum just laughed sarcastically. when shes at mine she doesnt wana leave and gets down wen her mum phones to say she is picking her up. n tbh i feel down wen shes gone aswell. i enjoy being with her and spending time with her. but what can i do to convince her mum im not just some shallow **** looking to get my wet? i was thinking of like sitting down with her mum and telling her how i feel bout my gf etc. but my girlfriend said she would find it emarressing. so im kinda stuck :S any ideas?