OP, I was going to suggest you do a cycling course, just to increase your confidence. It’s well worth checking out courses available in your area. If you’re not a confident cyclist, then I think this would be the first important thing to do, particularly if you are planning to be out and about with your kiddies.
I’m also on the family cycling group on FB. Again, this is a lovely place with lots of experienced people happy to share information. I’ve never used a trailer (couldn’t afford it when my DC were little), so can’t comment, but ask about and research this. Don’t be daunted or put off, there will be something available that will suit you and your family! One of my good friends used a beautiful Christiana box bike. Her three kiddies sat in the front box and she zipped about on that.
My kids are older now, but when my eldest was a baby (now 18yrs old!), I started out using a child seat with my lovely Specialised mountain bike (which I still have as I love it - it’s 26yrs old now and in perfect condition). Took a brief hiatus from cycling when I got my car license and got back into cycling when my youngest was about 4 or 5. Got a Halfords e-bike but found that I couldn’t fit a rear rack strong enough to have panniers and a suitable seat for dropping youngest to school (very annoying!). (Again something to research! See what fits with what bikes!!). I was left some money, took the plunge and got a Tern HSD. Not cheap, but it will take a passenger that weighs up to 60kg. With panniers and a front basket, there is more than enough space to take a good week’s worth of food shopping. I used to drop my youngest off at breakfast club and then zip off to work (beating the rush hour traffic). If I ever decide to give up my car, then the Tern will suffice for most of my car journeys (mainly local stuff, apart from occasional camping trips/long distance driving).
I think in your situation, I’d research what sort of bikes are around, how much you’d use it (and what for), the set up you’d like to use, what are the roads and cycle routes like in your area, what sort of storage you have available for it etc. logistics of putting it away etc. the Tern is great but bloody heavy, I use a ramp thing to wheel it in/out the summer house (I don’t have a garage). Also budget for helmets, gloves, high vis stuff like jackets and good security stuff for the bike.
E-bikes are bloody brilliant when you’re ferrying about kids etc, and I just have big smile on my face when I’m zipping about on my Tern. I feel like I’m 18 again!! It makes the hills a doddle too. I still have my Specialised bike but I love the step-through and upright position of cycling that my Tern offers. I used it today for commuting to work (just under 5miles each way).
FWIW, I don’t deck myself out in Lycra - today I wore my jeans, trainers, a sweater and my cycling jacket (plus cycling helmet and gloves). Should have bloody worn my over trousers and some shoe covers to keep feet dry from the spray, but never mind!
(sorry, that was stupidly long)