Learn Italian: Entrambi i bambini sono inseparabili e giocano sempre insieme. - Both children are inseparable and always play together.

Yes, you could say Tutti e due i bambini sono... It means the exact same thing as entrambi and also requires the definite article before the noun. Tutti e due is actually a bit more common in casual, everyday speech!

Inseparabili ends in -i. Does this mean it is a masculine-only adjective?

Not quite! The singular form is inseparabile. Adjectives that end in -e in the singular change to -i in the plural for both masculine and feminine nouns. Since bambini is plural, it becomes inseparabili.

Why is sempre placed directly after the verb instead of at the end of the sentence?

Adverbs of frequency like sempre (always) generally go immediately after the conjugated verb. Saying giocano insieme sempre would sound a bit unnatural unless you were trying to heavily emphasize the word "always".