I think you need to get sensible and think about the longer term gains and plans with your head - as at the moment you are in the moment with a very young child and some confusing (illogical) thoughts about childcare.
As general comments both your financial and housing situation are really precarious.
Paying 1k a month on debt alone on
lowish salaries is awful - not surprising you guys can't afford to run a household without living with your ex ( who presumably is paying half the mortgage and bills?). - you cannot afford to work just 2 nights surely!
Then you say the house is run down and needs work?
You are very clear that you don't see nursery as having g any emotional benefits to your child but can't see that being raised in a household with you current partner and your ex might be rather confusing?
You talk about needing a full time minimum wage office job but have a background at management level retail? Why are you going backwards in your career and accepting a lesser role?
If it's the partner on perm nights then that's something to address too - can you look at both of you stil being retail managers but working opposite shifts as far as possible thus minimising the need for FT childcare. I'm sure you will come back to say why this isn't at all possible but i suspect is because u don't really want to do that.
And finally - it's very easy for the person working less hours and having more downtime at home to say they are happy to forgo holidays or any of lives niceties - but when you are the partner doing the hard graft it's much less appealing to accept!
I suggest you start wuyh getting back to retail mgt and work with your partner to look at shift structures.
Hammer away at the debt and clear it.
Then look at housing situation - buy your ex out or sell and move
Either ensure you are independently financially stable or get married asap- if you don't and carry on as you are then you are in an increasingly precarious situation
Kids get more expensive and it's beneficial to be able to afford for them to partake in hobbies, travel, experiences and things like driving lessons when older
In terms of adding another baby to this mix - well, think this is more about looking for an excuse not to work more! I would aim to get working arrangements sorted for both parties, debt paid off and housing stabilised before thinking about this - you do have time on your side! With some focus you could look at when eldest starts school.
And finally - stop thinking about strangers raising children! Parents raise children - you are not sending them to a care home, it's an environment where they can learn and engage and make relationships with others, this builds independence, resilience and confidence. And even if you don't accept that it doesn't damage in the slightest.