Is this rude?

Well then your best is re booking second appointment for a different day....

I don’t think it’s unreasonable to ask someone to be on stand by, if this person is close enough to look after your child then they are close enough to understand that if a parent is free then they will take the place and that you are grateful but won’t need the help.

The OP has already clarified it is due to SN.
They really don't need to explain further.

People are so bloody weird on here. If she needs 2 parents to take the kid in the morning then she needs 2 parents to take the kid in the morning. We don’t know what the procedure is and we don’t need to know as that’s not the question. It’s not rude to ask someone to be on standby. It’s rude to expect it without discussing anything first, but you’re all adults! Just have a chat with family member and explain the situation. You don’t even know if the procedure is gunna be canceled so just go with the plan as it is and just let family member know that if it is cancelled then they are off the hook for having to help out.

@StripeyBalloon have you spoken to the hospital(s) about rescheduling one of the appointments?
they’re usually pretty amenable and quick - even just moving the second appointment to the end of clinic and explain the position.

then you could ask “family member” to bring DC along for transport to your location (unless it’s different places?) and one of you meet them there.

before I send “family member” with DC2 to the afternoon appointment, I’d check with the clinic if it’s acceptable for them to come without a parent or legal guardian present. They might not be able to see them without you there. Even something as simple as an eye test.

when I take my DC I’m always asked who I am, or my DC is asked who I am and say “my mom”, as if presence is consent.
granny/uncle might provoke a different response from the healthcare provider.

I do not understand why it would be rude to ask a family member to be on standby to take second DC to their appointment if needs be.

Surely you just explain the situation 'we both need to be present for DC 1, however if their procedure is cancelled, we can take DC 2 to their appointment ourselves, we will let you know as soon as we know'.

How hard is that?

It is a family member! Surely just ring and say what you said on here. I think sometimes when we are worried we can make unnecessary complications and this seems like one. No idea how it could be considered rude if you explain. If I was your mum and it was a treat afternoon with the second child I might feel disappointed not to go. But a medical appointment I would prefer the if need be arrangement.
Good luck, I hope all goes well

This

Your husband is massively complicating the thing. Anyone with a bit of sense would understand what you need. I would be miffed going out of my way to take sobeine else’s child somewhere if they could do it themselves. Can you not just explain this to family member and just ignore what your husband is saying

I'm not sure of the situation or what type of appointment it is but I work for a hospital that has a peadatric department and we don't normally allow family members who don't have parental responsibility/guardianship to bring children to their appointments so that might be something to query with the appointments office if the family member is going to bring them.

Why oh earth are you not doing kid 1 with mum kid 2 with dad

Seems weird

Who is looking after pm dc in the morning? Or will that one be at school?
In any case I’m sure family member won’t find it rude to be on standby if needed.

Do you not know what SN is?

Your DH is being a complete idiot. The favour you’re asking is for the family member to be on call in case they’re needed. Hospital trips aren’t fun for anyone, let alone people who don’t have to be there. If you explain to the family member that there’s every chance they won’t be needed, that will be perfectly polite. If they find out that they’ve had to rush around getting DC to an appointment while you were sat at home on the sofa, that would be really rude. It’s not a social occasion where you’re asking them to make themselves available in case you can’t find anyone better to go with!

Yanbu.
Your husband is dim not to get it.

It's not rude. It's not the same as a social occasion where failing to commit is rude. These are important appointments and you are trying to make sure both children get the best support possible.

Does it really need a detailed explanation?

YANBU. It might be rude if you took dc back to give them ice cream or something, but it’s totally valid to want to them back to take them due to an appt.

What do you mean by it takes two of you due to SN?

Your DH is being ridiculous. What I would do is have relative bring pmDC to the hospital, then you leave DH with amDC and do the appointment then relative takes him home. If amDC is already out of hospital could relative stay with DH while you go with pmDC?
It is better for DC if the parent goes so that should be the focus.

Presumably it is not particularly fun to do the appt so I'm on your side - I think it would be very rude to still expect family member to do it while both of you are sat at home.

However I am very confused by the whole thing - if it's you and DH doing it then it takes both of you but if it's family member they are expected to do it on their own. Why are there no school pickups (or need to be home for the taxi) in the mix? Presumably it is very complicated and you don't owe us all the details, but this is MN so you'll get a million different suggestions.

You both go to the morning appointment. Family member baby sits other child. Then 1 parent takes other child in the afternoon and other parent looks after child at home, surely?