Two hundred years before that hilarious farce The Play That Goes Wrong became a West End hit, Italian playwrights had come up with a similar comic formula, targeting the often disastrous nature of rehearsals before a show. Later, Gaetano Donizetti grabbed the idea and took it into the realm of opera, walking us backstage to witness the tantrums, jealousies, fist-fights and sheer panic that sets in when the clock is ticking inexorably towards curtain-up.

His two-act comedy Le convenienze ed inconvenienze teatrali this year joins a laudably long list of rarely heard works revived by Ireland’s Wexford Festival Opera since 1951. It’s a piece that fits perfectly into this season’s theme of “theatre within theatre”. Orpha Phelan’s brilliantly inventive new production, graced with a golden cast, has the whole house rocking with laughter from start to finish.

Canadian coloratura soprano Sharleen Joynt combines superb technique with great comic timing as the impossible prima donna Daria, who refuses to rehearse with a mere secondo soprano Luigia (Paola Leoci) – a decision that hastens the arrival of every director’s nightmare: Luigia’s domineering mother, Agata, played by the outrageous bass-baritone Paolo Bordogna. Agata steamrollers her way into the opera, shamelessly promoting her daughter, demanding cuts and rewrites and ignoring all objections. She can’t read music, sings badly, dances hilariously (even on pointe) and scatters cheerful catastrophe wherever she goes. It’s a wonderful performance.

Wexford’s new edition of this firecracker updates the 19th-century tradition of including in it music not written by the composer; the tenor Guglielmo (Alberto Robert) turns up thinking he’s rehearsing The Sound of Music. Later we get a very classy burst of Leonard Bernstein’s Candide. Amy Share-Kissiov devises some terrific dancing, and Danila Grassi conducts the festival orchestra with passion and precision. At the curtain call she wept as the opening night’s rapturous applause rang out; surely not the only tears of joy shed that night.

Compare Italian Giacomo Puccini and Anglo-Irishman Charles Villiers Stanford and they would seem to have nothing more in common than the year in which they died – 1924 – and yet both composers burned with a passion for opera. Puccini enjoyed wild success, amassing a fortune equivalent to $200m in today’s money, while Stanford found rejection, his works for the stage sinking almost without trace. You can hardly move for Puccini centenary revivals this year, but Stanford’s nine operas have had precious little attention. Justifiably so, some might say.

Wexford disagrees, and is honouring the Dublin-born composer by reviving The Critic, Stanford’s 1916 reworking of Richard Brinsley Sheridan’s 1779 satirical play of the same name. Stanford’s biographer Jeremy Dibble has produced a new performing edition of this surprising curiosity, which fits neatly into the festival’s theatrical theme. What immediately becomes apparent is Stanford’s evident impish sense of fun. He believed wholeheartedly in opera but plainly was not above mercilessly lampooning its pretensions, plots and stars.

Sneer, the critic, has been invited to witness a rehearsal of Mr Puff’s absurd new play The Spanish Armada, which composer Mr Dangle has transformed into an opera. These speaking characters comment on the action while singers portraying figures from the reign of Elizabeth I strut around the stage making ludicrously pointless gestures and getting in each other’s way. Sneer (Arthur Riordan) is quick to spot a flaw in the creaking plot: Walter Raleigh (Ben McAteer) and his comrades have already captured Don Ferolo Wiskerandos (Dane Suarez), son of the Spanish admiral, even though the fleet is nowhere in sight. Puff (Mark Lambert) brushes this aside: he needs to create a love story between the hapless Spaniard and Tilburina, the improbably named daughter of the governor of Tilbury fort.

Stanford reserves his best vocal writing for Tilburina, which soprano Ava Dodd exploits to the full, while the choruses swell with typical Stanford grandeur. Musical gags come thick and fast. Quotations from Wagner, Elgar, Beethoven and Parry pepper the score, and the increasingly desperate plot includes a lost-orphan-found moment parodying both Mozart and Sullivan. There’s even a portentous, doom-laden orchestral introduction to a character who neither sings nor speaks.

Conductor Ciarán McAuley has a lot of fun with those name-that-tune moments, while also caressing Stanford’s often luminously lyrical orchestral writing. John Comiskey has designed a handsome theatrical set, and director Conor Hanratty follows to the letter Stanford’s imprecation that the piece be played in all seriousness. “Any attempt to treat it farcically only spoils the humour.”

The season opened with Pietro Mascagni’s Le maschere, his 1901 bid to escape the shadow of his hugely popular Cavalleria Rusticana by honouring two Italian institutions: commedia dell’arte and the operas of Gioachino Rossini. It doesn’t really succeed in either aim, but director Stefano Ricci and choreographer Stellario Di Blasi give it their best shot, moving the action to a very 21st-century wellness centre. The plot is stock Rossini: father wants to marry daughter to unsuitable man; she has other ideas. It takes far too long to tell a simple tale, but some of the singing is excellent, particularly from sopranos Lavinia Bini as daughter Rosaura, and Ioana Constantin Pipelea as Colombina. Francesco Cilluffo conducts with Rossinian brio.

The three main operas are accompanied by some 70 small-scale recitals, lectures and new pieces over the 16 days of this most friendly of festivals. Chief among them is a contribution from celebrated Irish writer Colm Tóibín, who, with composer Alberto Caruso, has devised a witty, biting, one-act opera about Dublin’s Abbey theatre’s 1911 tour to the US with JM Synge’s controversial work The Playboy of the Western World. Lady Gregory in America is a beautifully fluent, lyrical hour, cleverly staged by Aoife Spillane-Hinks. A young cast is led by mezzo Erin Fflur as the redoubtable Augusta Gregory, making her defiant stand for art against US puritanism, alongside a standout performance from soprano Jane Burnell as the spirited actor Molly Allgood. Today’s America needs to see it.

Star ratings (out of five)
Le convenienze ed inconvenienze teatrali ★★★★★
The Critic ★★★★
Le maschere ★★★
Lady Gregory in America ★★★★

• Wexford Festival Opera continues at the National Opera House, Wexford, until 2 November