How to select records with a combination of values exist between two tables

Try the following query. first restrict the shipping rows to be only the valid ones, then join it to drawings

with valid as (
    select Max(ladready) ladready, ladjob, ladseries
    from shipping
    where ladjob=22925
    group by ladjob, ladseries
    having Count(*)=Count(case when ladready='Shi' then 1 end)
)
select v.LadReady, v.LadSeries, d.Job, d.Series, d.DShopStatus, d.SeriesInv
from valid v
join drawings d on d.series=v.ladseries 
    and d.DShopStatus='complete' 
    and d.status='shop issued'
    and not (d.SeriesInv in ('Invoiced','Part Invoiced'))

I don't know which dbms are you using, this is tested on MySQL and SQL Server.

Add below condition to remove all the LadSeries who are at least one time Yes

      Shipping.LadSeries NOT IN (
                                select distinct Shipping.LadSeries 
                                from Shipping
                                where Shipping.LadReady ='YES' );


select s.LadReady,s.LadSeries,d.Job,d.Series,d.Status,d.DShopStatus,d.SeriesInv
from Drawings d
inner join Shipping s on d.Job=s.LadJob and d.Series=s.LadSeries
where d.Job=22925
and s.LadReady='Shi'
and d.Status='Shop Issued' 
and d.DShopStatus='Complete'
and d.SeriesInv not in ('Invoiced','Part Invoiced')
and s.LadSeries NOT IN (
                         select distinct Shipping.LadSeries 
                         from Shipping
                          where Shipping.LadReady ='YES' )
group by s.LadReady,s.LadSeries,d.Job,d.Series,d.Status,d.DShopStatus,d.SeriesInv; 

                

Demo MySQL: https://www.db-fiddle.com/f/7yUJcuMJPncBBnrExKbzYz/177

Demo SQL Server: https://dbfiddle.uk/?rdbms=sqlserver_2019&fiddle=784990a572531ef9d4063926d8e55ec1

You can use a cte:

with cte(id, c, s) as (
   select s.ladseries, count(*), sum(s.ladready="Shi") from shipping s group by s.ladseries
)
select "Shi", d.* from drawings d join cte c on d.series = c.id and c.c = c.s where d.seriesinv = 'Not Invoiced'