" No person may leave or be outside of the place where they are living without reasonable excuse"
[Regulation 5(1), The Health Protection (Coronavirus, Restrictions) (England) (No. 4) Regulations 2020]
Regulation 6 provides exemptions which come within the definition of 'reasonable excuse'. Paragraph 12 (f) of that Regulation cites "for the purposes of informal childcare, for children aged 13 or under, provided by a member of a household to a member of their linked childcare household".
To form a "linked childcare household", the household that has one or more children (aged under 13) in it 'links' to a second household in order that the adult(s) in that household can provide informal childcare for the children from the first household. However, once that has been done, neither household can then form such a link with any other household, even if the original link is broken.
[Regulation 13, ibid]
So your sister-in-law is breaking the law every time she leaves her home to babysit on Saturdays or Sundays. (That assumes that she's already entered into a 'linked family household' to look after the other children when they're not at nursery). The reason that her daughter and son-in-law are going out on Saturday or Sunday evenings might also be relevant; unless they're going out, say, to do essential shopping, they'll also be breaking the law. (They can't leave their homes purely for social purposes).
Similarly, irrespective of the rules on 'gatherings', it's illegal to leave one's home to go and watch fireworks, as it's not covered by any relevant exemptions.
Further though, "No person may participate in a gathering which—
(a) takes place in a public outdoor place and consists of more than two people, or
(b) takes place in any other outdoor place (including any outdoor part of a private dwelling)and consists of two or more people"
[Regulation 9(1), ibid]
Regulation 11(2) provides an exemption from the above where "all the people in the gathering—
(a) are members of the same household, or
(b) are members of two households which are linked households in relation to each other"
('Linked households' are different to 'linked childcare households'; they can only be formed where one of the household only has a single adult in it, so it won't apply to your family members).
So, once again, the law is being broken by the group gathering together in a garden.