As you rightly say unless you can fit a 45 hours rest period every other weekend and still do the driving job you will only be able to legally drive one shift every other weekend.
Legally you must be finished the driving job on Saturday no later than 144 hours from when you started work on Monday, so if you started at 08:00 Monday you should be finished by 08:00 Sunday morning.
You also need to have a 24 hour rest period between finishing the driving job on Saturday and starting work the following Monday, I’ve no idea how anyone’s going to know if you have less than 24 hours rest but the law says you must 
By the way, as you’re working to EU regulations on Saturday the work you do from the previous Monday to Friday will count as other work for the EU regulations so you need to record those hours, legally the records should be on tachograph charts or printouts but unofficially the kind people at DVSA will accept records kept in a notebook/diary.
Goff118:
and is there any other advice for starting out with agency, for ad-hoc weekend work?
Probably the best advice about working for an agency is to believe nothing that you hear and only half of what you see 
Good luck and enjoy the HGV driving job