Not all men are in the discharge papers (for example, those who died in service). You would have to work out which regiments were there around this time (I can find references to the 51st, at least) and then look at the muster rolls to see if there was a possible Broughton there.
I would suggest you have a look for/try to obtain:
1. The actual marriage record for Jane, not an online index (witnesses may be some clue - did she sign or make her mark? etc.)
2. Any other Broughtons married or buried in the same location - potential siblings/parents etc.
Looking at the census, is she the one who married in Broughton Astley to John Shingles?
There is also an Elizabeth Broughton married there in 1823 to William Lawrence.
She may be the woman whose birthplace is listed in 1861 as "on the sea" in about 1801 - sounds like a possible for a military connection.
A military connection with the wife "on the strength" is often the most likely in terms of a bunch of children born around the place and then a return home with fairly "ordinary" occupations - in fact since the pension your average man got was not enough to raise a family on, it's quite possible he went back and continued in his old occupation - if possible.
If her father died in service, and her mother and the kids were out somewhere with the regiment at the time, a quick remarriage to another man in the regiment is a very likely scenario.
