I really struggle with this. I have a complicated medical situation and have very frequent hospital visits, at least 12 a year. I have to say I avoid the gp like the plague in order to cut down on how much childcare i need to find, and so yes I do go without. The medical service is there, but no, I can't access it as and when I see fit, I just can't.
I really can't do some appointments with either of them because the wait is usually too long and it's not fair on other folk in the waiting area, who are usually in as much pain as me. I'm frequently sent straight off after for ultrasound and blood, sometimes chest xrays which I really can';t take kids to of course. We're talking half days and more sometimes.
I also can't get what i need out of the appointments if they are there, and i've had ds2 howl with fear and rage at sight of some stranger laying hands on me each time i've absolutely been forced to take him. I would not want ds1 to hear what is being said as he would get wrong end of stick i'm sure.
I manage by mostly only arranging appointments at times I know I can cover most easily. The different clinics' staff are really helpful now they know me and will find me a spot in the middle of ds2s 2 nursery sessions a week. But I often have to cab it to make it.
I arrange with my mum to stay for a few of the big appointments in the year. My husband used to be able to shift work a little bit to help with one or two, but too busy now. It isn't willy nilly. It's an appointment - you know it's coming!
However, now ds1 is in fulltime school i'm finally able to properly trade childcare favours with other mum and kids i know well.
I don't think the professionals seeing us should have to put up with delivering inferior service to us if that's what they feel kids being present promote. But they have to cut slack in case of emergency. Now you know that they don't like it as a routine thing, you can always look around for someone who will tolerate it.