Vi ska träffa släkten på lördag om mamma mår bättre då.

Here ska mainly expresses a planned future action: Vi ska träffa släkten = we are going to meet the relatives / we will meet the family.

Swedish ska can sometimes suggest obligation too, like you are supposed to, but in this sentence it sounds most like a plan or intention.

Because träffa follows ska.

After ska, Swedish uses the infinitive form of the main verb:

• ska träffa
• ska gå
• ska äta

So:

• Vi träffar släkten = We meet / are meeting the relatives
• Vi ska träffa släkten = We are going to meet the relatives

Släkten means the relatives, the extended family, or the family on a wider level.

It is not exactly the same as familjen, which usually means the immediate family or household.
So:

• familjen = parents, children, close family
• släkten = relatives more broadly

In this sentence, släkten suggests a larger family gathering.

The -en is the definite ending, so släkten means the relatives / the family rather than just relatives in a general sense.

Compare:

• släkt = family/relatives as a general concept
• släkten = the family / the relatives

The definite form is used because the speaker means a specific group that both speaker and listener can identify.

Grammatically, släkten is singular, even though it refers to a group.

This is common with collective nouns. It works a bit like the family in English.

If you wanted to emphasize individual relatives, you might say släktingarna = the relatives.

So:

• släkten = the family / the extended family as a group
• släktingarna = the individual relatives

På lördag is the normal way to say on Saturday when talking about the coming Saturday or a Saturday in context.

It is a fixed time expression:

• på måndag
• på fredag
• på lördag

På lördagen is different. It usually means on the Saturday in a more specific context, or sometimes on Saturdays depending on the sentence.

So here på lördag is the natural choice.

In Swedish, family words like mamma, pappa, mormor, farfar, and so on are often used without a possessive when it is obvious whose family member is meant.

So mamma here naturally means my mum / mom.

This is very common in Swedish and sounds more natural than always saying min mamma.

Because må is the usual verb for how someone is feeling, especially in terms of health or well-being.

• må bättre = feel better
• må bra = feel well / be doing well

So om mamma mår bättre means if mum is feeling better.

Är bättre would usually describe something being better in a more general or objective sense, not so naturally someone's physical condition in this context.

Swedish often uses the present tense after om when talking about a future condition.

So even though the whole situation is about the future, the conditional clause stays in the present:

• om mamma mår bättre = if mum feels better

This is very similar to English, which also says:

• If mum feels better, we’ll go

not

• If mum will feel better, we’ll go

So the Swedish tense choice is very normal here.

Here om means if and introduces a condition:

• Vi ska träffa släkten ... om mamma mår bättre
  = we will meet the relatives if mum feels better

Be careful, because om can also mean about in other contexts:

• Vi pratar om dig = We are talking about you

So the meaning of om depends on the sentence.

Here då means something like then, by then, or at that time.

It refers back to på lördag.
So the idea is:

• if mum feels better by then / at that point

It helps connect the condition to Saturday specifically.

Without då, the sentence would still work, but då makes the timing a little clearer.

Yes. You can put the om-clause first:

• Om mamma mår bättre då ska vi träffa släkten på lördag.

When a subordinate clause comes first in Swedish, the main clause follows normal Swedish word-order rules, so the finite verb comes before the subject:

• ... ska vi ...

not

• ... vi ska ...

That is a very common Swedish pattern.