Her mother Angela Gordon, 35, and ex-partner Junaid Abuhamza, 31, were jailed in 2010 for her manslaughter.
Junaid Siddique batted 100 minutes for 27 as Bangladesh showed more resolve than in their first innings.
Broad's admission follows Graeme Swann's apology to batsman Junaid Siddique after sending him to the pavilion with a foul-mouthed outburst.
Imrul Kayes played a more measured innings alongside Tamim, and then we saw Junaid Siddique and Jahurul Islam rallying round as well.
Set 249, opener Junaid Siddique put Bangladesh on course with 55 and despite four for 63 from bowler Kemar Roach, Mahmudullah (51no) sealed it.
Junaid Siddique hit 100 for Bangladesh but the visitors, who had celebrated a great win over England last Saturday, posted a modest total of 234-9.
Junaid Siddique and Mushfiqur Rahim survived the morning with a 167-run stand before spinner Graeme Swann, who ended with figures of 10-217, ended that resistance.
Junaid reached his century off his 121st delivery, nine of which he hit for four, but lasted just two more balls, Kevin O'Brien claiming the wicket.
Number three Junaid and all-rounder Shakib Al Hasan rebuilt the innings from 28 for three, moving the total on to 135 before Shakib was dismissed by Stirling for 50.
To accompany the solid and experienced Umar Gul, they have the nippy, slingy Aizaz Cheema, plus left-armers Junaid Khan and Wahab Riaz, who can extract swing, in particular the reverse variety.
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Tredwell was fortunate to have the more circumspect Junaid Siddique on strike but scurried through his deliveries admirably, displaying great accuracy to concede just two singles from his opening three overs.
Iqbal, 20, struck 17 boundaries in his stand of 128 while fellow left-hander Junaid Siddique notched a career-best 78 and shared a second wicket stand of 146 to defy the home team.
Bangladesh deserve credit for the manner in which they set about their run-chase, Tamim working Zaheer Khan for back-to-back fours in the first over and Junaid Siddique pulling Irfan Pathan for six in the second.
Ex-partner Junaid Abuhamza, 31, was jailed indefinitely.
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Junaid Siddique and Shakib Al Hasan departed after attempting, and failing, to hit Johnston out of the ground, and Kevin O'Brien needed two attempts at first slip to give his former skipper the vital wicket of Mohammad Ashraful.
Junaid Siddique started aggressively, but became tied down and was leg before to Botha for 47 off 80 balls, to leave the visitors 140-5 and only a plucky ninth-wicket partnership between Mortaza and Abdur Razzak gave the score any respectability.
In the next over Junaid Siddique, having been thoroughly bewildered by the swing of Anderson, prodded one straight to gully and when Jahurul Islam edged Finn to Prior to make it 21-4, statisticians were reaching for the record books to look up Bangladesh's lowest score in Tests - 62 against Sri Lanka in Colombo in 2007.
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