Back in the Day solution
by Kegler

As indicated by the central entry, YOUNG AT HEART, the twelve answers that have animals at their centers get those animals' offspring as replacements before entry in the grid.

Back in the Day solution grid

Across
2BUT + C(HERS)HOP
10CREEd
11AUGER (ARGUE anag)
12BAA (1st letters)
13HI + B + ERNAL (LEARN anag)
15L + OFT
16GO + D + [M + OTH]ERS {LARVA for MOTH}
18C(R)OP
20LEIS ("LAYS" hom)
22K(AN + S.A.)'S
24E + RR
25FLO (1st letters)
32LEE (2 defs)
33SU(PER + FIN)E
34P.R. + Y
36MIL[L(I + ON] + TH)S {CUB for LION}
38AU + GUST
40ICERS (rev hidden)
42LO[CAT]ED (COLD TEA anag) {KITTEN for CAT}
45S[H(A)RE]D {LEVERET for HARE}
46MESA (SAME anag)
47IMP + ENDS
Down
1P[RO + BIN]G {CHICK for ROBIN}
2B + RIG
3TEE (2 defs)
4CARLOAD ("CARL OWED" hom)
5HUN + AN
6R[EEL]S (LEERS anag) {ELVER for EEL}
7HBO (last letters)
8OA[FISH]LY (SHY FOAL I anag) {FRY for FISH}
9PAT[H(OG]EN)S {SHOAT for HOG}
14BOO(N + [DOG]GLE)S (LOGGED anag) {PUPPY for DOG}
17AIRMEN (MARINE anag)
19RAZOR ("RAISER" hom)
21S[A(SS)]Y {FOAL for ASS}
23S + [COW]L {CALF for COW}
26ON(C)E
27S + T(O)IC
28RETHREAD (HARD TREE anag)
29R[OYSTER]S (SORRY SET anag) {SPAT for OYSTER}
30B + RISKER
31INtUIT
35RUB + LE
37TheEND
39I + TEM (MET rev)
41CEDE ("SEED" hom)
43OVA (hidden)
44D.A.'S (SAD rev)