Select random non-consecutive dates for every grouped element in R

I am currently trying to select non-consecutive dates for every grouped column.

In other words, I have the below dataframe:

I would like to basically group_by(Site) and then keep only 3 random non-consecutive dates for every grouped Site. For example, if HP37P1B has dates corresponding to 12th March, 13th March, 14th March and 7th March - I need a dataframe (for example) that only has:

HP37P1B 12th March

HP37P1B 14th March

HP37P1B 7th March

So far I have tried a number of stackoverflow posts that use diff(), ave(), and the lubridate package, but I haven't had any success.

EDIT

Based on comments below, I am trying to make this question reproducible

dput(uniqueSiteDate)

structure(list(Site = c("HP37P1B", "HP37P2B", "HP37P4B", "HP4008U", 
"INME03R", "INME03U", "INOA03R", "IPTO04R", "IPTO04U", "IPTO06R", 
"IPTO06U", "OLCAP2B", "OLCAP3B", "OLCAP5B", "PANMP1B", "PANMP2B", 
"PANMP3B", "STIN02R", "STIN02U", "UPMAP1B", "UPMAP3B", "UPMAP4B", 
"UPMAP5B", "UPMAP6B", "VAR210R", "VAR310R", "VAR310U", "VAR410R", 
"VAR410U", "HP36P1B", "HP36P3B", "HP36P4B", "HP4008R", "INBS04R", 
"INBS04U", "SEL107R", "SEL107U", "SEL207R", "SEL207U", "OLV110R", 
"OLV110U", "OLV208R", "OLV208U", "THEN10U", "HP37P1B", "HP37P2B", 
"HP37P4B", "HP4008U", "INME03R", "INME03U", "INOA03R", "IPTO04R", 
"IPTO04U", "IPTO06R", "IPTO06U", "OLCAP2B", "OLCAP3B", "OLCAP5B", 
"PANMP1B", "PANMP2B", "PANMP3B", "STIN02R", "STIN02U", "UPMAP1B", 
"UPMAP3B", "UPMAP4B", "UPMAP5B", "UPMAP6B", "VAR210R", "VAR310R", 
"VAR310U", "VAR410R", "VAR410U", "OLV110R", "OLV110U", "OLV208R", 
"OLV208U", "THEN10U", "HP37P1B", "HP37P2B", "HP37P4B", "HP4008U", 
"INME03R", "INME03U", "INOA03R", "IPTO04R", "IPTO04U", "IPTO06R", 
"IPTO06U", "OLCAP2B", "OLCAP3B", "OLCAP5B", "PANMP1B", "PANMP2B", 
"PANMP3B", "STIN02R", "STIN02U", "UPMAP1B", "UPMAP3B", "UPMAP4B", 
"UPMAP5B", "UPMAP6B", "VAR210R", "VAR310R", "VAR310U", "VAR410R", 
"VAR410U", "OLV110R", "OLV110U", "OLV208R", "OLV208U", "THEN10U", 
"HP37P1B", "HP37P2B", "HP37P4B", "HP4008U", "INME03R", "INME03U", 
"INOA03R", "IPTO04R", "IPTO04U", "IPTO06R", "IPTO06U", "OLCAP2B", 
"OLCAP3B"), Date = structure(c(18333, 18333, 18333, 18333, 18335, 
18335, 18335, 18338, 18335, 18338, 18335, 18333, 18333, 18333, 
18334, 18334, 18334, 18331, 18331, 18331, 18330, 18330, 18330, 
18330, 18332, 18332, 18332, 18332, 18332, 18325, 18325, 18325, 
18325, 18327, 18327, 18327, 18327, 18327, 18328, 18340, 18340, 
18340, 18340, 18340, 18334, 18334, 18334, 18334, 18336, 18336, 
18336, 18339, 18336, 18340, 18336, 18335, 18334, 18334, 18335, 
18335, 18335, 18332, 18332, 18332, 18331, 18331, 18331, 18331, 
18333, 18333, 18333, 18333, 18333, 18341, 18341, 18341, 18341,
18341, 18335, 18335, 18335, 18335, 18383, 18383, 18383, 18384, 
18384, 18384, 18384, 18385, 18385, 18335, 18342, 18342, 18341, 
18383, 18383, 18345, 18349, 18349, 18349, 18349, 18340, 18339, 
18340, 18341, 18339, 18386, 18386, 18348, 18346, 18347, 18328, 
18328, 18328, 18328, 18390, 18389, 18391, 18392, 18392, 18392, 
18392, 18392, 18392), class = "Date")), row.names = c(NA, -125L
), groups = structure(list(Site = c("HP36P1B", "HP36P3B", "HP36P4B", 
"HP37P1B", "HP37P2B", "HP37P4B", "HP4008R", "HP4008U", "INBS04R", 
"INBS04U", "INME03R", "INME03U", "INOA03R", "IPTO04R", "IPTO04U", 
"IPTO06R", "IPTO06U", "OLCAP2B", "OLCAP3B", "OLCAP5B", "OLV110R", 
"OLV110U", "OLV208R", "OLV208U", "PANMP1B", "PANMP2B", "PANMP3B", 
"SEL107R", "SEL107U", "SEL207R", "SEL207U", "STIN02R", "STIN02U", 
"THEN10U", "UPMAP1B", "UPMAP3B", "UPMAP4B", "UPMAP5B", "UPMAP6B", 
"VAR210R", "VAR310R", "VAR310U", "VAR410R", "VAR410U"), .rows = structure(list(
    30L, 31L, 32L, c(1L, 45L, 79L, 113L), c(2L, 46L, 80L, 114L
    ), c(3L, 47L, 81L, 115L), 33L, c(4L, 48L, 82L, 116L), 34L, 
    35L, c(5L, 49L, 83L, 117L), c(6L, 50L, 84L, 118L), c(7L, 
    51L, 85L, 119L), c(8L, 52L, 86L, 120L), c(9L, 53L, 87L, 121L
    ), c(10L, 54L, 88L, 122L), c(11L, 55L, 89L, 123L), c(12L, 
    56L, 90L, 124L), c(13L, 57L, 91L, 125L), c(14L, 58L, 92L), 
    c(40L, 74L, 108L), c(41L, 75L, 109L), c(42L, 76L, 110L), 
    c(43L, 77L, 111L), c(15L, 59L, 93L), c(16L, 60L, 94L), c(17L, 
    61L, 95L), 36L, 37L, 38L, 39L, c(18L, 62L, 96L), c(19L, 63L, 
    97L), c(44L, 78L, 112L), c(20L, 64L, 98L), c(21L, 65L, 99L
    ), c(22L, 66L, 100L), c(23L, 67L, 101L), c(24L, 68L, 102L
    ), c(25L, 69L, 103L), c(26L, 70L, 104L), c(27L, 71L, 105L
    ), c(28L, 72L, 106L), c(29L, 73L, 107L)), ptype = integer(0), class = c("vctrs_list_of", 
"vctrs_vctr", "list"))), row.names = c(NA, -44L), class = c("tbl_df", 
"tbl", "data.frame"), .drop = TRUE), class = c("grouped_df", 
"tbl_df", "tbl", "data.frame"))

To answer other questions, sometimes there are more than 3 dates per site, but sometimes there is just 1 date per site. But the idea is to choose n Number of non-consecutive dates given a Site. In other words, if a particular site has 4 dates, I need 3 non-consecutive ones. If a particular site has only 1 date, let's just leave that in.