Here's what I've culled out for Caroline:
1853: William Slater, ship carpenter, r Palmer above Queen
1854: Caroline Slater, b.h. (boarding house) Palmer above Queen
1855: Caroline Slater, b.h. Palmer above Queen
1856: Caroline Slater, b.h. Palmer above Queen
1858: 136 Coates
1859: 302 Callowhill
1860: Caroline Slater, boarding house, 302 Callowhill
1861: Caroline Slater, bh, 302 Callowhill
1862: 458 N 4th
1863: Caroline R Slater, boarding house, 323 New
1864: Caroline Slater, boarding house 323 New
1865: Caroline Slater, boarding house 323 New
1866: Caroline Slater, boarding, 335 Dillwyn
1867: Caroline Slater, wid William, h 335 Dillwyn
William Slater, clerk, h 335 Dillwyn
1868: Caroline Slater, wid William h 335 Dillwyn
1869: Caroline Slater, wid William, 335 Dillwyn
1870: Caroline Slater, wid Wm, 335 Dillwyn
William B Slater, wheelwright, 335 Dillwyn
1871: Caroline Slater, wid Wm, h 335 Dillwyn
1872: Caroline Slater, wid Wm, 335 Dillwyn
John F Slater, machinist, 335 Dillwyn
Wm. B Slater, wheelwright, 335 Dillwyn
1873: Caroline Slater, wid Wm., h 1047 N Front
John F Slater, 335 Dillwyn
Wm B Slater, wheelwright, 335 Dillwyn
1874: William B Slater, wheelwright, 335 Dillwyn
I quit following her after 1873. I think she ran a boarding house and the 1870 census seems to support that. I used the city directories that are on Fold3. I'll take a look at the link you provided.
Charles seems to have had many occupation: ship carpenter, shipwright, carpenter, grocer, produce, builder, butcher, and farmer.