Articles: Put clean socks on before we go to visit Grandma.

The article before Grandma is not necessary.

Yes, Grandma can be capitalised.

ReegisIs it grammatically correct to omit an article before Grandma?

It would be incorrect to put an article there. We don't put articles before names unless "the" is part of the name or we want to emphasize the name for a purpose such as sarcasm.

Hmmm, but is Grandma a name? Like Jane or John?

I understand this sentence as:

Put clean socks on before we go to visit your grandmother.

Put clean socks on before we go to visit Grandma.

Grandma is how the children address their grandmother.

It is not wrong to say "Put clean socks on before we go to visit your grandmother."

ReegisPut clean socks on before we go to visit your grandmother.

That is quite formal. It's either to impress on the kids that grandmother must be respected, or perhaps indicating an "unfriendly" or formal relationship.

Grandma is frequently a name that kids call their grandmothers.

Grandma here is used as a name It requires an initial capital letter and no article.

(Crossposted with AS)

Now it is clear:)

Thanks tamguatlay, AlpheccaStars and fivejedjon for the explanation.

Keep the socks clean before we visit Grandmother house....

That is not natural in this context, and does not mean the same as the original.