As above, you absolutely must accept the offer (check how you do this, some LAs require you to officially accept with either them or the school, some assume you are accepting the place unless you let them know otherwise).
It would be madness not to accept something, even if you're not overly happy, as it would leave you without any place at all, but it would especially be madness as you say you are happy with what you have been given anyway. Any place is better than no place and accepting it does not mean you can't go on the waiting list for other schools. No place at all means you may end up eventually having to take something miles away. Admissions only have to help you find a place once, and they've done that (your second place no less, some don't even get that!). They won't help you again if you reject the place, you'd be on your own.
It works differently in each LA re waiting lists. Some you go on automatically for any preference school listed higher than the one you got, others you have to ask to go on it (it's not first come first served so no immediate rush, you're all ranked according to the admissions criteria for that school, so can move up or down the list depending on who else goes on or off the list. Second round of admissions is not until May, then there'll be another round in June and then July). The information for what you need to do regarding waiting lists should be on your LA website.
Wait it out. You may get lucky between now and September as plenty of people do move about. Depending on where you are, some who have been offered a place at the school you want may turn it down to go private, some may move out of the area and no longer require that space etc (but likewise, other people may move in and live closer, moving higher up the waiting list than your child). If you don't get offered a place, be thankful you've been given your second preference which you are satisfied with. I'm sure your child will be fine wherever they end up.