How to say “Greetings to your family”

I’m writing a birthday card to my japanese host mother from last year and at the end I wanted to say something like “greetings to your family as well!” or “I hope you and your family are all doing well.” or something like that.
But I don’t really know how to say that in a quite natural way.
( Also, my host mother speaks English so it’s fine if it’s not a 100% naturally sounding sentence, she will still understand what i’m trying to say. )

ご健勝をお祈りします (ごけんしょうをおいのりします)
It literally means "I am pray

ご健勝をお祈りします
(ごけんしょうをおいのりします)
Go-kenshou o oinorishimasu
It literally means "I am praying for/wishing for your (good) health (wellness)"

@nina:
i am not op, but just for my curiosity: is this phrase only used in written conversation or can i tell it also to someone orally?

Is it possible to say it, yes, but it might sound stiff. If you want a greeting to say then it might be cliche, but "genki" is common and best way to go. A good phrase is:
お元気でいらっしゃいますか。
O-genki de irasshaimasu ka?

ご健勝… is for written letters, and is very formal.

The OP says he wants to write it at the “end” of the letter – so putting a question at the end might not quite flow right.

I would suggest something like:
ご家族の皆さんも、お元気でいらっしゃいますように。(I hope that everyone in your family is doing well.) 私からよろしくお伝えください。(Please send my best regards to them.)

You are writing to your host mother but want to make sure your message is forwarded to the whole host family, am I right?

If so, just add "minasan" (meaning "everyone on your side") at the top of whatever you want to say to them.

Examples:

みなさんのご健勝をお祈りします

みなさん、お元気でいらっしゃいますか。

Hope it helps.

Another phrase for writing could be:
皆さま、お変わりないことと存じます。
Minnasama, okawari nai kototo zonjimasu.
It is hard to translate to English well, but it is telling her "I hope your family does not have a hard time" or "I hope your family stays well/is well"

Thank you very much!