Advice needed on babies and visas - Please help! (Mexico City)

So here is my story, please share your experiences and/or advice:

I'm living in Mexico City with my mexican partner. I'm still on a tourist visa and have been here for about 4 months. I work from home for a US company. I recently discovered I am pregnant. now 3 months, not planned but we are very happy and keeping the baby.

INITIALLY I wanted to move back to the UK to have the baby and raise BUT its just impossible for my partner to get a visa. I need to be working earning over 22k gbp a year and can prove that for 6 months to qualify.. firstly I've not been working so can't prove it. I would never make that kind of money in the UK so it just doesn't work. We are not rich we live day to day so any sort of student visas are ruled out and I don't even think he would pass the English test for the entry.

Which leaves us staying in Mexico and raising the child.
I really don't want to keep living in Mexico City with a baby so we are looking into moving to Playa Del Carmen.

Now the Advice Part:
In your opinion should I go back to the UK and have my baby while my partner is on a 6 month tourist visa and then return to Mexico when the child is around 3 months
OR have the baby in Mexico...

VISAS - I read that if i have a baby in Mexico to a Mexican national I automatically qualify for a permanent residence visa and right to work without having to prove any earnings.
Does anyone know if I can go straight to permanent if i have my baby in the UK?
If not do i need to go through the temporary residence for 4 years situ? Or maybe 2 years if we get married?

I'm so confused with the whole situation. I know having the baby in Mexico would make my future here easier and i could visit my family upto 6 months in the uk after the birth but in the UK its free health care and i don't know the costs on having a child here because we would need to rely on our families help with everything money wise which is a huge burden

thanks for reading
Lucy