Does anyone actually read what the OP has posted? It is not a question about her paying the childcare by herself vs 50% from each partner etc.
She states "The whole reason I am going back is because we can't afford to live off DP wages alone".
Therefore she has to go back to work to earn some money as currently the household is not making ends meet.
But, as she states "If I was to use my wages alone to pay childcare fees I would actually be losing money to work , especially when factoring in petrol , work clothes etc".
The total household income will not cover current bills, plus the increase in childcare costs, no matter if one person pays 100% or if both of them pay 50%.
OP, look into practical suggestions from others who have actually read your post. Tax free childcare, childminders are normally cheaper than nurseries, especially if they can take your older one after school as well, can you (or your OH) do your 37 hours over 4 longer days?
Even if you are only just breaking even until the 30 hours free childcare kicks in when your baby turns 3, it is worth it for the career continuation, pension, NI etc etc.