Thanks Skinny for an enjoyable puzzle. Definitions are underlined in the clues.
Across
9 Rocking robin, huge one seen next door (9)
NEIGHBOUR : Anagram of(Rocking) ROBIN, HUGE.
10 Crown represented in a coat of arms? (5)
CREST : Double defn: 1st: …/top of a mountain or hill; and 2nd: A design at the top of a coat of arms, distinctive of a family or corporation.

11 Scoff vegetables, no good on reflection (5)
SNEER : Reversal of(… on reflection) “greens”(vegetables that are, well, green in colour) minus(no) “g”(abbrev. for “good).
12 Lager drunk after spirit, drinker’s penultimate drink (6,3)
GINGER ALE : [Anagram of(… drunk) LAGER placed after(after) GIN(a spirit/a strongly alcoholic drink)] + last but 1 letter of(…’s penultimate) “drinker“.
13 Mastic’s moulded, not in the right part (7)
MISCAST : Anagram of(… moulded) MASTIC’S.
Defn: Said of, say, an actor who is playing a part/role not suited to him/her.
14 Noblewoman‘s party venture (7)
DOWAGER : DO(a party/a social function) + WAGER(a bet/a venture/a risky undertaking).
Defn: … with a title derived from her late husband.
17 Carry out purchase picked up in city (5)
DUBAI : Homophone of(… picked up) “do buy”(to carry out/to effect a purchase).
19 27D notebook (3)
PAD : Double defn: 1st: Solution to 27 down/where one is staying.
20 Inception filmed here? (5)
ONSET : [ON SET](at the place with stage scenery, furniture and other articles where a movie is filmed).
21 Girl‘s not much wearing fancy hat (7)
TABITHA : [A BIT](not much/just a little) contained in(wearing) anagram of(fancy) HAT.
22 Scheme involves close to twenty exercises in which small children can lark about (7)
PLAYPEN : PLAN(a scheme/a plot) containing(involves) last letter of(close to) “twenty“ + PE(abbrev. for “physical education”/physical exercises).
24 Advocate a couple of drinks (9)
SUPPORTER : [SUP(to drink) + PORTER(a dark brown bitter beer)](a couple of drinks).
26 Wheels on a New York taxi may be so worn out (5)
TIRED : Double defn: 1st: Describing the wheels on a NY taxi, fitted with tyres, or tires as spelled in America.
28 In France, he’s swallowed by lake of purplish hue (5)
LILAC : IL(in French “he”) contained in(…’s swallowed by) LAC(in French, a lake).
29 It’s rude to have house-warming without one (9)
INSULTING : “insulating”(to have a house interior warmed/protected against the cold) minus(without) “a”(the article for “one” in number).
Down
1 We are responsible for this load (4)
ONUS : [ON US](we are responsible/we take responsibility for something, as in “the damage is on us”).
2 Various rivals of Tom Daley (6)
DIVERS : Double defn: 2nd: …, the champion diver.
3 Livestock here help, so it’s said, to supply a drug dealer (10)
PHARMACIST : Homophone of(…, so it’s said) [“farm”(where livestock are/found here) + “assist”(to help)].
Defn: One who could be whimsically (or cruelly) called a drug dealer.
4 Have no recollection of counterfeit tobacco’s origin (6)
FORGET : FORGE(to counterfeit/to copy illegally) + 1st letter of(…’s origin) “tobacco“.
5 A relation of K-Pop? (8)
GRANDDAD : GRAND(a 1000 dollars or pounds/abbreviated to 1K dollars or pounds) + DAD(like “pop”, an informal term for one’s father).
No relation to granddad … nor grandma for that matter:

6 Spots one charged with arson at last (4)
ACNE : ACE(“one”, as in the number of pips on an ace playing card) containing(charged with) last letter of(… at last) “arson“.
Defn: … on one’s skin, especially on the face.
7 Makes unstable grenades explode (8)
DERANGES : Anagram of(… explode) GRENADES.
Defn: … mentally.
8 Lacking nucleus, fermenting yeast is swelling (4)
STYE : Anagram of(fermenting) [“yeast” minus its middle letter(Lacking nucleus …)].
Defn: … on the edge of an eyelid.
13 Core component of racism I’d studied (5)
MIDST : Hidden in(component of) “racism I’d studied“.
Defn: …/the middle of.
15 No one knows a terrible place for tropical birds, according to Spooner (3,3,4)
WHO CAN TELL : Spoonerism of(…, according to Spooner) [“toucan”(a species of tropical birds) + “hell”(a terrible place of great suffering)].
16 Betray public official, almost retired (3,2)
RAT ON : Reversal of(… retired, in a down clue) [“notary”(a public official authorised to perform certain legal formalities) minus its last letter(…, almost)].
18 Party game in which a well-known Christian hides very quietly under container that doesn’t close (3-5)
BOB-APPLE : [BALE(Christian, a well-known award-winning actor) containing(hides) PP(abbrev. for “pianissimo”, musical direction to play very quietly)] placed below(under, in a down clue) “box”(a container) minus its last letter(that doesn’t close).

19 Insect burrowing into unvariegated banana (8)
PLANTAIN : ANT(an insect) contained in(burrowing into) PLAIN(unvariegated/uniform/bland).
There are bananas … and there are bananas:

22 Expression wears thin when spoken (6)
PHRASE : Homophone of(… when spoken) “frays”(wears thin, as with, say, fabric).
23 Some lepers I abandoned in ancient land (6)
PERSIA : Hidden in(Some) “lepers I abandoned“.
24 Very keen on being spoiled regularly (4)
SOLD : 1st, 3rd, 5th and 7th letters of(… regularly) “spoiled“.
Defn: …/having been persuaded to be enthusiastic about something).
25 Stroke, not the first that hurts (4)
OUCH : “touch”(to stroke/to move one’s hand across a surface) minus its 1st letter(not the first).
Defn: Exclamation expressing “…!”
27 Very much approves of excavations (4)
DIGS : Double defn: 1st: …/appreciates very much; and 2nd: …, at an archaeological site, say.
This was a good example of an excellent crossword in the category “Let’s Not Make Things Too Complicated”.
Elegant, and precise too.
Many thanks to scchua for the blog & Skinny for a very sound puzzle.
A very enjoyable puzzle coupled with an enjoyable and colourful review. The clever 5d was my favourite.
Many thanks to Skinny and scchua.
Nice to see the setter progressing so well. I enjoyed solving this and particularly liked the rocking robin (cue for a song?) and the 1d responsibility.
Thanks to Skinny and to scchua for the review.
I thought this was excellent for a relaxing Sunday morning, with amusingly-constructed wordplay. I’m not normally a fan of Spooner-related clues but 15D was magnificent. Thanks Skinny and Sschua.
Many thanks to scchua for the excellent blog, and to all who commented – it’s greatly appreciated.
A really good puzzle which I had the pleasure of solving last night. Plenty to like, but I must single single out 5d and 15d as my joint favourites — both very clever and both raised big smiles.
Many thanks to Skinny and to Scchua for the review. Both much appreciated.