On the other hand, maybe she is struggling to have a relationship with you alongside the weight of work and her child. Moving in together will enable her to have that relationship. If you think you could have a future with her, then you need to make the extra effort to make things work around her burdens.
I realise everyone will disagree and say "don't be a pushover" etc but sometimes women aren't playing games and are just hopeless at managing their responsibilities. It would be a shame to give something up which you could fix.
Yes totally agree, its tempting to be "Alpha Male" and just dump her and move on....potentially, not the grown up way to go though. Relationships are hard.
For background, we live 15 miles apart...overwhelmingly its me going to her. She's come for a night out in my town once in the last year. She's come over to stay with her kid another 10 times or so. I go to hers once a week, at least. The other week she was ill so i rushed over to hers to take her kid out for the day (i was off work already) with my own 2 kids. Often i cook when at hers, and buy the food too.
So, i feel i pull my weight.