Siyempre hindi ko alam ang buong story so let me give my POVs based on what you mentioned. Eto mga sumagi sa isip ko.
1) bakit sa bf ng tita mo iniwan ang anak niya at hindi sa inyo or any kamaganak? Maybe she has her own reasons. As I see it, he's being groomed to be the child's step father na.
2) How can he be an "ex"? Leaving her child with him means sila pa rin.
3) Leaving her child with him means she trusts him and has forgiven him of his battering. Kung yung Tita mo napatawad yung bf niya, everyone should respect that.
4) The fact na may honors ang bata, it means that his (to-be, or already) step dad is doing well in supporting his studies.
5) mukhang maayos naman ang pangangatawan at spirits ng bata under his guardian's care.
6) Hindi na mama's boy ang bata. This should be seen as positive. He can get along with his guardian and even the family of the guardian.
7) Masakit yung sinabi niya about relating his achievement to the absence of his mother pero bata pa lang siya. Hindi pa siya sensitive enough to choose the right words to say. Maybe it's not what he means, I'll give him that. If however, marami na siyang nasabing ganun ang dating, then that's when I will start getting alarmed.
8 ) What do you mean "mapapel is ex-bf"? If it's bragging about the achievement of the child, I'll take that as positive. Proud siya sa alaga niya like any parent.
9) His threat na hindi makukuha ng Tita mo ang bata dahil siya ang naghirap, walang basis yon. The real parent still has the right ano pa man ang sabihin niya. Don't take that seriously.
You can't blame the child kung mas mapalapit at gustuhin manatili sa tito niya kasi 1 year na silang magkasama at masaya naman siya dun. Of course, magiging mas familiar siya sa relatives ng tito. Your Tita should have predicted this before she chose the rightful guardian for her son.
Let your Tita communicate more with her son. Sa skype, she should say remarks like "Anak I'm proud of you, hindi nasasayang ang pagod at paghihirap ko sa pagpapaaral sayo" She should establish sa anak niya na siya ang nagpapaaral sa kanya. You show yourself more to your cousin also like invite him to occasions o gimmick na malapit or convenient sa kaniya para hindi sila makatanggi. You may also send him congratulatory gifts or little stuffs like activity books or items of his interest (not necessarily expensive) just to let him feel na present kayo and you care for him kahit bihira niyo siya makita.
Mahirap malayo sa sariling anak. Any small scale situation namu-multiply dahil sa pagkasabik at pagaalala niya so please, hangga't maaari, i-balance niyo yung balitang ipaparating niyo sa tita mo.
I do understand may mga issues na nakakalungkot pero I hope you also see the lighter side of it.