Yes as long as, on days/weeks you drive in-scope of EU regulations you comply with the daily and weekly rest period requirement for the EU drivers regulations there’s nothing to stop you working 60 hours a week for a month.
By the way, on days/weeks that you drive in-scope of EU regulation the care work will count as other work for the driver hours regulations but will not count towards the 48 hour average working time rule for mobile workers WTD (The Road Transport (Working Time) Regulations 2005).
There is a 48 hour average working time rule in the general Working Time Regulations 1998 (your care work WTD) but unlike the drivers rules it can be opted out of.
I agree with @les_sylphides if you want to be taken seriously it may be worth changing the topic title 