merging child-table date range with parent - sql

Question

I asked a similar question in the past, and imagine there is already an answer for this, but I can't seem to figure out the wording to locate it.
I have a parent table with a date range and a child table that can have multiple date ranges within the date range of the parent table. I need to merge them into a row for each record in the series. An example should better explain what I'm trying:
Table 1 (Parent)
Date1 Date2 Person
1/1/16 7/1/16 A
and
Table 2 (Child)
Date1 Date2 Person
2/1/16 2/4/16 B
3/6/16 3/8/16 C
5/4/16 5/9/16 B
I want a merged table like so:
Merged Table
Date1 Date2 Person
1/1/16 2/1/16 A
2/1/16 2/4/16 B
2/4/16 3/6/16 A
3/6/16 3/8/16 C
3/8/16 5/4/16 A
5/4/16 5/9/16 B
5/9/16 7/1/16 A
There must be a somewhat easy way to do this? I'm fine with a complicated while loop, but am stumped on the logic for this too.

Answer 1

As requested, this is a modified version which considers multiple PK/FK
Declare #Table1 table (PK int,Date1 Date,Date2 Date, Person varchar(25))
Insert into #Table1 values
(1,'1/1/16','7/1/16','A'),
(2,'2/1/16','8/1/16','A')
Declare #Table2 table (FK int,Date1 Date,Date2 Date, Person varchar(25))
Insert into #Table2 values
(1,'2/1/16','2/4/16','B'),
(1,'3/6/16','3/8/16','C'),
(1,'5/4/16','5/9/16','B'),
(2,'3/1/16','3/4/16','B'),
(2,'3/6/16','3/8/16','C'),
(2,'5/4/16','5/9/16','B')
;with cteBase as (
Select *
,Gap1 = Date2
,Gap2 = Lead(Date1,1,(Select max(Date2) from #Table1 Where FK=PK)) over (Partition By FK Order by Date1)
From #Table2
)
Select PK,Date1,Date2=(Select min(Date1) from #Table2 Where FK=PK),Person From #Table1
Union All
Select FK,Date1,Date2,Person from cteBase
Union All
Select FK,Date1=Gap1,Date2=Gap2,Person=B.Person
From cteBase A
Join #Table1 B on FK=PK
Where Gap1<>Gap2
Order by PK,Date1
Returns
PK Date1 Date2 Person
1 2016-01-01 2016-02-01 A
1 2016-02-01 2016-02-04 B
1 2016-02-04 2016-03-06 A
1 2016-03-06 2016-03-08 C
1 2016-03-08 2016-05-04 A
1 2016-05-04 2016-05-09 B
1 2016-05-09 2016-07-01 A
2 2016-02-01 2016-03-01 A
2 2016-03-01 2016-03-04 B
2 2016-03-04 2016-03-06 A
2 2016-03-06 2016-03-08 C
2 2016-03-08 2016-05-04 A
2 2016-05-04 2016-05-09 B
2 2016-05-09 2016-08-01 A

Answer 2

Perhaps something like this?
Declare #Table1 table (Date1 Date,Date2 Date, Person varchar(25))
Insert into #Table1 values
('1/1/16','7/1/16','A')
Declare #Table2 table (Date1 Date,Date2 Date, Person varchar(25))
Insert into #Table2 values
('2/1/16','2/4/16','B'),
('3/6/16','3/8/16','C'),
('5/4/16','5/9/16','B')
;with cteBase as (
Select *
,Gap1 = Date2
,Gap2 = Lead(Date1,1,(Select max(Date2) from #Table1)) over (Order by Date1)
From #Table2
)
Select Date1,Date2=(Select min(Date1) from #Table2),Person From #Table1
Union All
Select Date1,Date2,Person from cteBase
Union All
Select Date1=Gap1,Date2=Gap2,Person=B.Person
From cteBase A
Join #Table1 B on 1=1
Order by Date1
Returns
Date1 Date2 Person
2016-01-01 2016-02-01 A
2016-02-01 2016-02-04 B
2016-02-04 2016-03-06 A
2016-03-06 2016-03-08 C
2016-03-08 2016-05-04 A
2016-05-04 2016-05-09 B
2016-05-09 2016-07-01 A