Sammy,
Very tricky situation.
How long has your Fiancee been living in the UK - presumably 4 years
The best option is to get married first. After this there will be two options,
1). Your husband 'sneaks' out of the country and then applies for Spouse entry visa at his home countries BHC, DP or consulate. This assumes that he was not served by any deportation orders
2). Do an in-coubtry 'fight' to legalise the stay - be prepared for a lengthy fight...but having a child and a home will be a big plus on your side......you will have to involve a solicitor and your MP
Before you make any decision - Please consult a Solicitor/legal advisor as your case will have to be handled outside the rules...
Best of Luck - and dont forget to send us some cakes
Where there is a will there is a way.