What word could I use to describe somebody who is getting on with a difficult life changing situation and making the best of it. Brave is not quite right but nearly there. Stoical is not right either.
The New Oxford American Dictionary has very nice “the right word” sections. Here is the one located under the entry for courage:
For myself, the noun I would use for this would be endurance, but looking it up in my favourite dictionary showed that the adjectival form (endurant) is not so commonly used. Nonetheless, I think it quite captures what you are looking for.
How about using "resolute" or "determined"? In particular I think the former might be a good match because it combines aspects of both "brace" and "stoical". Somebody who has resolved to do something is going to step out and continue doing what it takes to get it done even if the road is hard and they don't wear a perpetual smile. Being resolute implies that emotions are under control or even held back in order to persist at the task at hand. This certainly takes a kind of courage or bravery that isn't rash or fleeting.
And with the aid of a thesaurus you will find that there is a rich selection of words that generally fit the theme. The variety seems to indicate that the concept strikes a chord with the human condition. Here is a small selection: persevering, intrepid, undaunted, valiant, persistent, relentless, assiduous, audacious, gallant, indomitable.
Perseverance might fit the bill. From M-W:
continued effort to do or achieve something despite difficulties, failure, or opposition
The emphasis here is on repetition: an effort that persist in face of many difficulties. Although, it can be applied to a single effort if you want to describe an attitude or if a single effort is composed of many small steps (and life changing ones usually are).