@Toria33 , I'm sorry for your losses. Congratulations on your DS and your new pregnancy.
From the perspective of professionals, these scans are medical assessments of your pregnancy and need to have professionals fully focused on the scan rather than potentially being distracted at important points by another child. The 12 week scan is used for dating and for measurements for screening for conditions, some of which are life-threatening - it's important to be as accurate as possible.
As you and I (and many others) are sadly aware, sometimes people get bad news at scans. Advising people against bringing their other children along means that, if someone is told bad news, they can at least process it and have any necessary discussions without also having to be responsible for another child.
I'd really suggest trying to find someone who could look after your DS for the appointment, even if just for the duration of it. They could sit with him in the hospital grounds or coffee shop if necessary - I would be happy to do that for a friend if they needed it.
If you absolutely can't find anyone, and you need your DH with you in the scan (it's ok to need someone with you, I absolutely needed my DH with me for scans during a pregnancy after loss), you can and should still go for the scan, and for any other appointments where you can't get childcare. If you speak with someone in advance (there should be a number on your appointment letter) and then explain when you arrive, then they'll know what to expect and may have their own ideas about how to support you. For example, they may have a student in the unit who has 10 minutes free to sit with your DS, or a quieter room for you to sit in if you're anxious.
As you've seen, sometimes people do need to bring children along. It's not advised and it's not the preferred option, but it happens. If you have no alternative, then just try to mitigate the effects through advance notice and making sure DS is fed, changed, settled, etc if possible.
Pregnancy after loss can feel so stressful, and can bring up lots of difficult emotions. Have you spoken about this with a midwife yet? There may be additional help available, like specialist psychology support or a midwife who specialises in this area. There are also support threads available here on MN, which may be worth checking out.