I think you're getting confused about the 'inheritance of two alleles' thing - there are a huge number of genes that control coat colour and pattern acting in various loci on the chromosomes, so the dog doesn't just inherit two full stop, it inherits two copies of the allele for each gene iyswim.
Hair colour is created by two pigments - eumelanin (black/liver) and phaeomelanin (red) - but a huge number of genes control these these pigments and therefore dictate the coat colour and pattern.
In your example the black dog is BbEe (dominant black carrying for liver, gold carrying but not expressed); these genes, and the agouti one for 'and tan' which he must also have, are found at different loci on the chromosome. Therefore the gold bitch in your example can also carry for liver and 'and tan'
The below is my understanding of it in the case of my dogs...
My liver pigmented (therefore liver carrying) red bitch produced black, black and tan, red and liver in a litter to a black dog.
She is bbeeKkatatSS (bb=liver carrying, ee=homozygous red, Kk=no tan points herself but can produce it, atat=can produce and pass on tan point and SS=solid coloured doesn't carry particolour). She *could* be kkatat (tan pointed) and they are not visible due to the extension e gene (red) masking it, but I'm assuming she isn't.
The dog in this case is BbEeKkatatSS (Bb=black carrying recessive liver, Ee=heterozygous non-red, dominant E stops it being expressed but recessive e can be passed on, and KkatatSS same as my bitch).
My liver pigmented gold dog has produced gold, red, liver and black when mated to black bitches. He is bbee (liver carrying, homozygous red). He hasn't produced particolour when mated to a bitch that previously has so I'm assuming SS. I don't know about tan but based on his lines I doubt it.
When he has been mated to a liver pigmented red bitch they only produce red/gold puppies. Both of them are bbee and in all their pups the recessive e extension gene prevents the extension of eumelanin (the black/liver pigment) in the hair follicle so all the pups are red/gold. Their pigmentation (eye rims and nose) shows the 'true' colour (liver in this case).
When mated to a liver bbEE bitch all the pups were liver as they were all bbEe and the dominant E extension gene allowed the extension of the black/liver (bb liver in this case) pigment.
A liver son and daughter from a black bitch have produced black, gold and liver (not together
) and a black son from a black bitch has produced black, red, gold and liver to a gold bitch.
The gold litter sister of the abovementioned black son recently produced a litter containing solid black, solid liver, liver roan and black and white when mated to a blue roan dog. Ro doesn't carry parti but I know that the dam does as she has previously produced it.
