MT - your position is quite similar to that of my dh. He also had few formal qualfications before he started. (He had a few O'levels, but no A'levels to speak of.) We didn't have kids while he was doing his degree, though, and I have huge admiration for you in managing to do your degree, and to do so well, while bringing up a baby. I hope that whoever's writing you a reference is making all these points on your behalf. It strikes me (at least, this is what I'd argue if I were your referee) that it's entirely plausible given your situation that you haven't yet hit 'terminal velocity' and therefore that you are just going to keep on getting better and better.
(The fact that you asked your dp to push you is no excuse for the way he has made you feel bad about this. Anyone with an ounce of empathy would have realised that you'd have done the feeling bad bit for yourself, and what you really needed was a pat on the back and some congratulations for what is, honestly, a huge achievement.)
I was also going to say, re. applying to other departments, that you should bear in mind that you don't actually have to be on the doorstep of the place where you're doing your PhD (I'm assuming, since you classified it more as humanities than sciences, that it doesn't involve lab work or suchlike). I have a student now who lives over an hour's drive away. She normally comes to see me about once every 3-4 weeks (and we're in touch in between by email) and she attends a pg training course roughly once a fortnight. Again, my dh commuted quite a long way to do his PhD. It's not ideal, but it is do-able.
Good luck, once again.