OP - like you and a lot of Mums on here Ive been through this and its hell - but I promise it passes. Usually the first year is worse and then the immunity builds
If you have a good employer they can generally see you are committed and doing your best and they allow for it. Not sure what type of work you do but if you are able to WFH and catch up out of hours they can usually tell and appreciate it. If you do shift work or work which has to be completed on site then its so much harder.
You don’t say if your employer is showing signs of wanting to act on your absence or not but I agree with other posts, I’d get a head start on addressing the problem pro-actively, before they do.
Your employer cannot dismiss you for taking time off to care for dependants so firstly ensure you communicate all agreements in writing in case they decide to act.
You are allowed unlimited dependant leave - you are legally allowed to take any day off to care for your dependants when ill or in case of emergency. These days are unpaid so its a cost financially but cant be used in absence calculators for disciplinary. However the law does state ‘reasonable’ time so the employer might act by implementing an absence improvement process if they felt that time was becoming disproportionate or unreasonable compared to others. You may want to keep evidence that your child was sick (such as messages from nursery or doctors notes) just in case.
Parental leave is available as a statutory right but, honestly, its next to useless as you have to plan for it and we don't know when our DC will be sick! You book blocks of time off in advance - you can take 4 weeks per year and up to 18 weeks in total of parental leave until your DC reaches 18. You still accrue holiday entitlement as usual while on parental leave. However if your employer becomes difficult then planning some parental leave time over the flu season might be a good idea. You can book parental leave but change it with 7 days notice. You cannot be disciplined for taking parental leave but they can refuse the request with a fair business reason however.
Both options above are difficult for both you and your employer to manage and utilising them often may build up resentment on the employers side.
I think your best option is to put in a flexible work request - if you feel your employer would be amenable and the business could accommodate your job on different hours. Flexible work requests could be to agree to work a set number of hours but you are responsible when those hours are worked, giving you the opportunity to catch up evenings or weekends and not lose pay. Other options include compressed hours - working longer days over 3/4 or working 5 days but some long/short daily hours, giving you flexibility to arrange working days around calls from nursery. Some employers offer a buy back holiday scheme so you can add more holidays and take a pay deduction spread over 12 months.
Flex work may mean a salary reduction but it can be small if planned properly. You risk going into unpaid leave currently so its worth calculating the cost options. Employers can decline your request but only if theres a genuine business reason and they risk a discrimination claim if they cannot prove that you couldn’t do your job just as well on a flexible work scheme.
Finally - childcare! It may be worth speaking to nursery and putting in a policy. I agreed with my childminder I would come collect for viral, high temperature or sickness but not a runny nose or cold. Children constantly have colds and staying away from nursery wont prevent other children from getting sick as children are contagious before symptoms start with most colds. Generally kids are fine with Calpol in the morning :)
To work full time with no support, be a caring parent and juggle life can’t be easy. I really admire you and good luck x