Homeddays, no need to panic! Trust your instincts as you absolutely do not have to do anything that resembles school at home.
The fact that you have read about unschooling probably shows that you do not feel a particularly structured approach fits your children! The reason DD wants to 'just watch TV all day' could be for a number of reasons...making up for lost time by having it restricted previously by virtue of being at school for most of the day, a cultural fear that TV is wrong (and worse, non educational!) or simply that she is easily able to learn in this way. TV will spark many different interests and 'allowing' her to watch it will not mean this is all she ever does - she will have her fill and find other things to do when she is ready and has a desire to.
Watching TV for my DD inspired a whole series of activities linked to Inuts. This included a 1950's BBC documentary on you tube that led to a small child version of global warming discussions, igloo crafts with salt dough, playing various Inuts games (ox push for example) so if I was thinking in school terms, we managed to cover loads of history, geography, science, maths, English, art and PE...all because of one small thing on TV!!
You can definitely unschool and still have limits of bedtimes, good etc...though you can also read and learn a little more which may or may not take you away from these things. That is the beauty of HE, you can really relax and facilitate an education that suits your children. Only you will know how long you plan to HE and what your hopes for your children are in future. There are lots of Facebook groups which might help too, as well as interesting blogs if that's your thing.
Child-led is child led, it is not not giving them a choice of things you might like them to do/think are suitable (this is what they got at school and doesn't suit everyone!), as the poster up-thread suggests. If you are happy to facilitate them being child led then that's great, if you feel you might like them to do 10mins or so per day of an online programme too then that's great too - think about what is best everyone and work out a plan!
The grandparents issue is not easy, but once you have decided on the approach that is best for your family, you could always give them some reading or discuss how it will work.
Saracen is right and ALWAYS has wonderful advice, as do loads of others on here! The suggestion of day trips is great, perhaps actives like these would also give breathing space from grandparents and spark various interests that your DC then want to pursue via other avenues.
Enjoy 