The Cordelia Dream, Wilton's Music Hall, LondonWell, Apollo Shaftesbury, LondonMary Goes First, Orange Tree, Richmond

'King Lear' springs to mind in this heavy-handed story of a poisonous family relationship, but it only serves to remind us of what we're missing

Has the dramatist Marina Carr been having trouble with father figures? A nameless Woman rings insistently on the doorbell of her dad's bedsit in The Cordelia Dream, Carr's new two-hander for the RSC. To borrow a term from the literary critic Harold Bloom, Woman appears to be suffering from "the anxiety of influence". The Old Man is a composer and so is the daughter, and following in parental footsteps has led to estrangement.

Whenever the father is writing successfully, we gather, the daughter cannot – and vice versa, though he, being the more competitive, has the worse case of symphonist's block. He has demonised her as "the dog-hearted ingrate", scorned her output, and holed up like a mad hermit with only a sleeping bag, his piano and a white-tie outfit for the moment of glory which he still imagines will be his when his masterwork is complete.

The two leads acquit themselves well, given the material. David Hargreaves's silver-bearded Old Man manages to be charismatic and viciously crushing – a casual misogynist. Michelle Gomez's Woman switches between forlorn child and vengeful spirit. At times, with her hooded eyes, she darts towards his face like an adder planting a poisoned kiss.

The more immediate problem is the playwright's relationship with her forefathers in the literary canon. The RSC's commissioning policy could be enriching, inviting contemporary playwrights to use historic works as a springboard. But, alas, this writer is C-rated. Heavy-handedly, Carr has father and daughter discoursing on famous lines in King Lear. The Cordelia Dream seems to fancy itself wryly sophisticated and attuned to primitive urges. In truth, it is tedious and clumsy.

Surprisingly, perhaps, Well, a play about invalids and hypochondriacs, has gone from strength to strength. A seriocomedy by the US dramatist Lisa Kron – about her sickly mother and the writer's own stint in an allergy ward – it had a small-scale premiere at London's tiny Trafalgar Studios. Now, in one bound, it has transferred to the Apollo on Shaftesbury Avenue.

Veteran Sarah Miles makes a stage comeback playing the dramatist's mother, Ann. An eccentric old bird, she snoozes under a rug on her La-Z-Boy recliner, yet perks up regularly to bustle up to the apron stage and rabbit to the audience.

Meanwhile, her irked daughter, Lisa (Natalie Casey), is planning to stage a play based on her experiences, "a theatrical exploration of health and illness, both in the individual and the community", as she explains. Thus Well becomes a tongue-in-cheek variation on Pirandello's games with pretence and reality, as the mother casts doubt on the accuracy of her daughter's memories, and the daughter is in turn pummelled by a childhood bully whom she wanted to expunge from her flashbacks.

Most thought-provoking are the doubts raised over self-deceit and the label "psychosomatic" which Lisa – after seeing a shrink – uses to explain symptoms. That said, the mock disarray into which Casey's presentation descends serves as an excuse for a hopelessly ill-structured ending. Casey is excellent as the sassy daughter, with explosions of screaming rage, but Oliver Chris (from Green Wing) is disappointing in his minor roles, playing an oldster with an unconvincing stoop. The West End promotion of Eve Leigh's low-budget production draws attention to the play's weaknesses.

Mary Goes First at least provokes a few chortles. The Orange Tree, known for reviving forgotten gems, has dusted off this 1913 satire by Henry Arthur Jones, and Auriol Smith's staging seems set to develop into a trenchant exposé of political corruption along the lines of Ibsen's An Enemy of the People.

Two businessmen are jostling to run a northern industrial town. Sir Thomas Bodsworth (Philip York) is the Tory mayor, newly knighted, but the sanatorium he has built is engulfed in scandal. Richard Whichello (Michael Lumsden) is at loggerheads with Bodsworth and threatens to run in the next election as a Liberal.

Meanwhile, his wife, Susie Trayling's Mary, enters into unscrupulous negotiations over cash for peerages. This ensures that Jones's play remains topical. Disappointingly though, it dwindles into a petty drawing-room comedy, centring on Mary's bitching about Lady B's dress sense. A sharper director would have let in more darkness, especially in the final act where Mary's humiliated rival weeps. Instead we get excessively light entertainment.

'The Cordelia Dream' (0844 800 118) to 10 Jan; 'Well' (0870 890 1101) to 24 Jan; 'Mary Goes First' (020-8940 3633) to 31 Jan