Advice on a birthday present after not speaking

So I have a family where’s nothing ever seems to Ben simple. Since my 10th birthday in 2001, I lived with my dad and stepmam (until I move down to uni in 2011, and then dor a few month after leaving uni and getting my own place). I have two blood siblings, one half and one full, both through my real mam. Due to stuff that went on (while in her care and afterwards), I never spoke to my real mam, unless I saw her in the street and then that was out of politeness but my two sisters had been in touch (full sister tried living with her but the night had nothing more to do with her after a bit, half sister was in touch with her a lot later). Anyway, my real mam passed away just before my half sister’s birthday last year (her 18th). It was my half sister who found out as she wasn’t the last person my mam had called on her mobile. She Goldman’s me as i got out of work (I believe it was a Thursday), and I arranged to take the Monday off whenever I went in on the Friday as, although we didn’t talk, i was my man mam’s oldest child. So I stayed with my dad and stepmam (they live in the next village along), and arranged to meet her next of kin, a guy calle Shaun (bar my half sister who doesn’t only recently come back into her life, she had alienated everyone else). I met with Shaun and another lady, who did my mam’s cleaning, at my mam’s bungalow and he told me that she’d said nobody was to go in the house or attend her funeral as everything was for the dog shelter (fair enough). My half sister corroborated this and gave me the same story. Lo and behold, the day beforehand the funeral her conscience must have pricked her and she asked if I would be attending the crematorium with her and her aunt. This shocked me so much as she had waited until then, knowing full well all along she was going to attend. All I ever wanted was clarity. Since then, we only spoke about three weeks before Christmas for five minutes. My problem is that she has told me so many lies (I wouldn’t have minded her telling me the truth, I would have understood), when was left some stuff (again, I don’t mind being but it’s the lies), and the only time she got in touch was when she usually would receive her Christmas present in the post. Now it’s her birthday next month and, the human in me who has been hurt says don’t go to the lengths of getting her anything, as I’ve never even received a card off her on birthdays and Christmases, but the part of me who is a brother says I should. What would you guys do in this situation? Do you have any advice?