I personally think greeting someone as soon as you arrive to their house is a reasonable expectation. I don’t think that saying “hello” to the host is unusual request. Do you find it unreasonable?

Having said that, I don’t blame you not wanting to go there. I wouldn’t either. One thing if it was his house and mom lived there due to advanced age. Entirely different thing if if it’s her house. I’d rather stay in my own place or go on dates in neutral places

If she puts a pressure on you, it’s unpleasant. But if you don’t go there, it should not effect you at this point. Not a reason to not break up. If you want to end, just end it. No point in dragging it