OP in the nicest possible way, you have to stop blaming the government, your parents (I know you haven't said this outright, but the implication is there) and your employers and take responsibility for the problem that you both MUST deal with.
Try to look at it practically, without emotion. You both have to work, your usual childcare option is not available. What could you do?
Beg your parents, that's unfair and they'll still say no,
Not work, no, you need money,
Work from home, not an option if you're a teacher, particularly so if you're also caring for young children, few employers will accept that now,
Change your hours, go part time temporarily, both of you need to speak to your employers to see if there's any flexibility,
Nursery? None available nearby,
Before and after school care, hours don't work and they're full,
Get a childminder, or two, have you even looked into this? No more expensive than a nursey and they will do school runs,
Nanny, too expensive, or is it?
Au pair, not enough time to organise
Friends, ok if short term, but expect to reciprocate in babysitting favours, or offer to pay,
Neighbour, I know some who help out their neighbours if need be even if they don't have young kids.
So I think you should speak to your employers about starting later and look into a childminder or a nanny.
This is an issue facing so many parents. Lots of people had to work outside the home during the initial lockdown with zero childcare options, if they could do it then, you definitely can sort it now.
Oh and ignore your parents saying not to use external childcare, it's none of their business, and what do they expect you to do?