I see this used by a father to refer to his two male children. Why isn't it iad? As in, e.g., seo iad mo mhic?

And if it's because chlann is singular, why isn't it é, since they are male?

You could make a better argument for iad: sid iad mo chlann mhac.

If I had the chance to do so, I would encourage you to work your way through a textbook, like Teach Yourself Irish.

I'm not a fan of seo é - isn't it sid é?

Why not "siod"? the d isn't slender as far as I know.

I'd say "sin mo mhic". Sin mo pháistí and sin mo chlann are right too.
The use of é/í/iad isn't mandatory, at least in Ulster, which would solve your problem

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Because the word "clann" is grammatically feminine?

I would think that, when using a collective noun such as "clann," grammatical gender and number would be the default.

Redwolf

Apparently, 'that is the congregation' is correctly: sin iad an pobal.

I don't know if Tobar na Gaedhilge will yield examples by native speakers saying *sin é an pobal. Maybe in some parts of Ireland they had that? I can't be certain, so I won't overegg the pudding.

As far as I know, the following are correct:

sin iad an mhuintir
sin iad an pobal
sin iad an aicme

Whether clann is seen as collective in the same way is an interesting question, to which I have no answer.

Anyhow, you can ditch clann and say: sin iad mo bheirt mhac, which is definitely right.

I'm not sure why it is written with a broad d in some dictionaries. Does it etymologically derive from seo+rud? And so because the d of rud is broad, some dictionaries write the word with broad d?

Anyhow, the only syllables coming after it are: é , í, iad - all of which slenderize the previous consonant, so the realization is: sid é, sid í, sid iad. See also the caid é pronunciation of cad é, and compare Ulster goidé for confirmation of the slender d...

That may be the realization everywhere? I don't know, however, but it would be interesting to find out either way. I wonder if Bríd can tell us if she says sid í or siod í, ie sidí or siodaí in terms of pronunciation?

Learning Irish (Cois Fhairrge dialect) simply has Seo é/í, no mention of seod.

Iorras Aithneach (West Conamara) has seod é. (Interestingly, there is an example seod é an áit a rugadh é ... ("That's where he was born") Why é? Because they are talking about a particular house (teach, which is masculine) in the preceding sentence.)

Some English grammarians insist on singular agreement for collective nouns, but Irish tends to see them as "lots of people" (common usage in English often does too).

Tá an saol mór ina gcodladh "Everyone is asleep" literally "the whole world is in their sleeping".

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

The English usage depends on where you're from. In the U.S., collective nouns are always singular (in fact, we call it "the collective singular"). British usage tends to favor treating them as plurals. I can't speak for other English-speaking areas.

Drove me crazy when I read "Watership Down" at the age of 10 and encountered the phrase "the council were merciful"!

Redwolf

Don't worry. It's all behind ya now.