Was I rude not to go on the sunlounger when she offered?

[Obsessedwithstitch]

Took my Dd to the beach this morning, we put towels down fairly close to the sea, I didn’t pay for a sunbed as they’re expensive and was only planning to stay a couple of hours.
Dd met a boy around her age and started to play by our towel. Boys grandma came over and apologised and said to send him away if I felt I was getting dumped upon, She was really nice and I assured her it was absolutely fine and nice for them to play with each other.
She went back to her lounger and came back down to us ten minutes later and said she had the sunlounger next to her free (you pay for two together and the parasol/shade) and asked if I wanted to use it/sit there and was very welcome to.
I wasn’t sure what to say and said ‘Erm, no I’m alright, it’s ok, thank you for offering though’ she looked a little embarrassed,
Afterwards I felt a bit mean and unfriendly, she was perfectly nice, but I really didn’t fancy making small talk for a couple of hours on a lounger next to a lady i’d only just met.

Am I a misery?

I mean, she could have meant I use the lounger and sit away from her…just the whole situation would have been a bit awkward I feel
I felt mean and like I was being unfriendly though, I literally couldn’t come up with a reason/excuse quickly enough as to why

No. Her wish to be sociable didn't align with yours not to be. It's just one of those things that happens. Slightly awkward to recieve an unwanted invitation, slightly awkward to have your invitation declined, but no one was in the wrong.

She offered, you declined - you don't have to accept every offer that's made to you. Will she think you are a bit rude ? Possibly, who knows? More likely she's given it no further thought. In any case you'll never see her again, so what does it matter ?

Yanbu.

Rude

She probably just wanted to keep a closer eye on her grandchild, as she was looking after him at the beach.

That was her chance to do so, she didn’t know you either.
Neither party is wrong, but I’d say that’s why she asked.

You weren’t rude. You politely declined. I would’ve done the same.

It wouldn’t have been a closer eye on him though? Beds are up at the top looking down at the beach, we both could see them easily but me sitting where I was, was an even closer eye on my Dd/them

You weren't at all rude and I suspect you are overthinking it.

She offered, you politely declined. That's all there is to it. Very few people would want to share a parasol and second sunbed with someone they'd only just met.

No, you were polite and clear.