Apologies if this sounds harsh, but if I was to read this post in isolation, I would presume you were an internet troll who had joined to try cause an arguement by posting an outragious story.
I'm not saying you are, but this story, well it's going to get some reactions alright, and mine may be mild in comparison to some.
I am though going to try to be helpful.
Firstly to your actual question - asking are you reasonable to ban your girlfriends child from what will be her house. Ermmmmm!
Really, the fact is, if you meet a new partner, and she has children, then they come as part of the package. I can't think of any half decent mother would accept such a proposal really.
Moving on though to the bigger question which this has thrown up however, let's look at a few facts here
1. You once bought a house together. When you had arguements, she would go to her sisters and lock you out, instead of talking it through and resolving your differences like relationships usually demand to be successful.
2. She talked about you to her son in the local language. Well how do you know she was talking about you for sure? If she was though, that's beyond rude and not a good sign (ps start to learn this language, if only a few words so you can keep track)
3. You sold the house but you have been supporting her and her son since you went home. Erm HELLO!
4. You haven't been supporting her as much as her last boyfriend. Well to know this, she must have told you, and told you in some detail. I'm sorry, but I spent some time in Thailand and I got to know some bargirls socially and their mentality. Your girlfriend doesn't sound like a filipina, she sounds like a bargirl.
We get cultural things coming in here, most filipinas want to and prefer to work, why should she need "supporting". Why are you expected to support her?
Sorry but this is REALLY ringing alarm bells.
5. Your relationship hit a low enough for you to sell the house and move back home, BUT now she wants you to buy another house for her? I bet she bloody does!
Look, really I wish you the best and I want things to work out for you, and I can't allow for your feelings if this "love" thing has taken over, but come on - she has more baggage than Heathrow. This relationship just doesn't seem to inspire confidence.