It is not fully correct, but it is very close.
If you want to make the instruction softer than imperative, then present conjunctive (also called subjunctive) is a good way to go.
It is more like "may you remember" than "remember!", if that is what you are after.
In idiomatic English you wouldn't usually use "may you" — the Latin conjunctive is far less heavy.
See this question about the difference between these two moods.
For "do not forget" your translation ne obliviscaris is excellent if you go with conjunctive.
The form of commemoras is indicative, whereas the conjunctive would be commemores.
The indicative means a factual statement "you remember", which is not a guidance or an order, so that is out of the picture.
The bigger question is whether his is the verb you want.
We have a list of free online Latin dictionaries.
For the ones that have English to Latin translation, you can check out options, and any of them will do for checking whether a verb has the tone you want it to.
Here are some options:
- commemorare: call to mind, be mindful of, keep in mind, remember, recall, relate, mention
- memorari: remember, be mindful of
- recordari: think over, bethink one's self of, be mindful of, call to mind, remember, recollect, think of, meditate, ponder
(This one comes from cor, "heart", if that matters.)
- scire: know, understand, perceive, remember
- fovere: keep warm, cherish, foster
- meminisse: remember, bear in mind
These are just some that came to mind.
Commemorare is a good choice, but it is up to you to decide whether there are better ones.
You told in a comment that it is the most suitable one for you, but a future reader looking for a similar motto might prefer something else.
Semper is a good translation for "always", and it makes sense to balance the two sides of the whole phrase so that both have a verb and smaller word of some kind.
To better mirror semper, you could also use numquam ("never") instead of ne ("do not").
You can also play with word order.
Chiasm — inverting the word orders in the opposing parts of the phrase — is my suggestion, but not necessary.
The only crucial part in the word order is to have numquam and obliviscere together and also semper and commemora together.
Within these word pairs you can do as you like.
To keep the two pairs separate, a comma or a row break will help.
So, one option with conjunctive would be:
Numquam obliviscaris, commemores semper.
[May you] never forget, [may you] remember always.
Inclusion of "may you" is optional.
I just wanted to describe the tone by that translation option.
If you want imperatives, use obliviscere or commemora instead.
So, to make it more of a recommendation than a wish, you could choose:
Numquam obliviscere, commemora semper.
Never forget, remember always.
Based on the comments, I think this is the best offer I have.
But please wait for others to weigh in before making a final decision.