Holidays / travel - help!

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Hi! Hoping for some advice regarding travelling with a 3 month old. Heading to spain for a week and am suddenly panicking... Does anyone have recommendations of a cheap / lightweight pushchair which is suitable?
Also car seats - is it necessary? We don't plan on driving but is this needed for coach transfers?
If we have a car seat does this come on the plane with us? If not how did you carry your little one in between? I'm in a bit of a panic - fly out in just over a week and feeling very underprepared! Thanks in advance for any advice you can offer!

We used a silver cross zest but I noticed in the Argos catoglue that they have a copy of it by their own brand cuggl which is much cheaper.

It's a while ago now but we had a Chicco stroller for holidays that could be reclined almost flat for DC. In most cases you keep your pushchair until you get to the plane and then it's loaded into the hold. You usually can't collect it until it comes through with the suitcases so will need to carry DC from the plane to the baggage hall.

We always took our own car seat as we tended to hire a car and I preferred to have our own. You can just check it in with your cases, we had a big bag for it that made it easier to carry and padded it a bit with spare towels.

Not sure what you would do with a RF car seat on a coach transfer though as they mostly have a lap belt. I think most people just hold the baby on their laps for the transfer but someone else may know more.

Perfect - really useful thank you