We went June last year with kids (10 & 8) and had a fab trip. We hired a car and drove to Vik on the south coast, which was a pretty coastal village great as a base for diamond beach/jokulsarlon glacier lagoon, and some waterfalls. In the town was a public pool, with some thermal pools, we spent an enjoyable afternoon here, and an excellent Lava/volcano exhibit. We then did the golden circle, finishing in Reykjavik, were we pottered, visited the pool again (excellent for kids) and went to Perlan, a science/geology museum, where there was a northern lights style show. The cafe there does massive ice creams, that were a huge hit. Our kids particularly liked the geysers, and the Reykjavik pool. It was a great trip all round, and v child friendly.

We went in April a few years ago with a 5 and 10 year old for four days. It was cold, but not unbearably so, it was very windy. We all wore lots of layers (bought cheap base layers from decathlon and waterproof over trousers, both of which were useful). We hired a car so we could go at our own pace and stayed in self catered accommodation outside of reykjakik (we stayed in two different places over three nights to make the car journeys shorter). We were lucky that the weather was fairly mild so all roads were passible and we made it to jokulsarlon (which was amazing). The kids enjoyed the many stop offs at huge waterfalls, Vik was great, and every corner gave new impressive views. We did not see the Northern Lights, we thought the kids too young to do a tour where you spend all night driving round, we stayed somewhere pretty remote and outside of the city so were hoping we might just be able to see them if we got up in the night but it wasn't to be.

The boys remember and talk about the big waterfalls and fun little things that happened on the trip. As adults me and my DH loved it.

@ginforall, my husband and I plan to go back, just us, once the kids don’t want to holiday with us anymore. Then we can drive the whole ring road, visit the villages on the east and north coast, and do more hiking than we could with kids. As adults, I think an Iceland holiday would be different.
But for the OP, it’s still a great one with kids. Forget to mention the Blue Lagoon (the kids still laugh at the ‘Krap slushies’ they got there), and my wee boy still reminisces about the Icelandic hot dogs that we bought as our post pool snack. Like gin said, it’s the little things they’ll remember.

I think they would like it, but Iceland is hella expensive for everything so don’t forget to factor that in. There is a geothermal swimming pool that is really cheap in most towns. IMO the blue lagoon is worth it. There is a really cool hot river you can go in guidetoiceland.is/connect-with-locals/regina/reykjadalur-hot-spring-valley-in-south-iceland which is an easy hour’s hike, but not sure if it would still be snowy in April.

Watching with interest! We were meant to go in April 2020!

It's traditionally horrible weather over Easter. There is even a special word for the typical cold, wind, hail and rain (páskahret). I've never seen a nice Easter and I've been here for over a decade (though I was abroad for a couple of those Easters so in fairness I might have missed a good one). Mid-April is really the tail end of winter rather than spring. The snow has melted and everything is brown and soggy. March and April are probably the ugliest months for this reason, in my opinion, although the daylight situation is good and of course the landscape is still beautiful on a sunny day. Things improve a lot in May when the new greenery starts to come through. See this local waterfall in April - it's quite nice despite the brown sogginess, but it's much nicer in the green summer or a frosty/snowy winter's day!

Mind you Easter is rather late this year so it's a reasonable bet, as Easter goes. If you have the option to come in summer, though, I would recommend that much more.

We went in end of April and got a lot of "window pane" weather it was start of spring/summer and pretty nice. In the sun it was lovely and warm but you did need to wrap up when in the shade.
I think May or June would be nicer.

We did a really fun bike tour of the town, Got a hot dog from the famous stand, saw puffins out at sea!
Rode Icelandic ponies and did a day in the blue lagoon

All super fun...

We went a few years ago in March with 5 and 2 year olds. Was great. Fresh snow but not too cold. Saw the northern lights. Expensive but not particularly difficult as far as travelling with kids goes.