One of my areas of expertise is infectious disease, including Parvovirus B19 (Fifth Disease). This is NOT the same variant of Parvovirus that infects dogs and cats, and you can NOT get it from an animal, so don't worry about your pets. Also, there is no vaccine available for this virus.
Please ask your obstetrician to order Parvo B19 IgM and IgG tests immediately. Although your son's symptoms appeared when you're at 20 weeks, he was most infectious about 10 - 14 days before you saw his first symptoms, which puts you about between 18 and 19 weeks. This is still a risk period for complications to the fetus.
Here's how the tests are interpreted. If you have presence of only IgM or of both IgM and IgG to Parvo, you are recently infected. The likelihood is that you will have no symptoms, although some adults can develop a type of transient arthritis from the virus, which usually only lasts a few weeks, but can last for up to a year or more. The risk to your baby, however, is high. Your obstetrician will need to monitor the baby's development closely by ultrasound to make sure that fetal hydrops is not developing. If it does, this indicates that the virus has infected the fetus and is destroying the blood-forming "machinery." The danger of this is that the baby can become anemic and inadequate oxygenation because of this can lead to later learning and developmental disorders. In most cases, hydrops is not severe and the pregnancy can proceed normally to term. If it is severe, a specialist can do an in utero blood transfusion, but this can be a dangerous procedure, because there is risk of fetal hemorrhage and miscarriage.
The good news is, that more than half of all women of childbearing age have already had Parvovirus and are immune. If the test shows only IgG antibodies to the virus, you have nothing to worry about. The obstetrician may still prefer to be cautious and do a couple of extra ultrasounds, in case the IgM window was missed, but if you get the test done now, that's not likely.
Since your son's rash has faded, he's no longer contagious. Your 4 yr old, however, could be in the viral prodrome phase now, and very well could be contagious. While the risk is lower now that you're at 20 weeks, I would still send him off to Grandma's for a week or two if you can bear it.
When you ask the doctor for the Parvo testing, ask him/her to also test for CMV immunity. Most obstetricians are still not aware that this poses a significant risk to pregnant women who are around small children (which you are), and 1 of 150 children are born with congenital CMV which can cause severe birth defects and life-long health problems. The testing is the same for Parvo (IgM and IgG), and the interpretation is the same. You can reduce risk to yourself from both of these viruses by practicing simple precautionary methods, which everyone should do, anyway. Namely, never kiss a small child on the mouth, and wash your hands frequently -- especially after exposure to nasal mucous or oral saliva.
If your doctor wants to learn more about CMV (definitely should, if he/she has not already counseled you), the Association of Public Health Laboratories is hosting a webinar on the subject this Tuesday at 10AM PDT, 1PM EDT. The cost is only $95 ($115 if you want access to the video archive), and can be accessed from https://www.aphlnet.org/eweb/DynamicPage.aspx?webcode=Eve...
If the link doesn't work, go to aphl.org, and scroll down through the professional development area to "education and training." Select "webinars." On this page, there is a link on the right with the training calendar. The CMV webinar is the first item on it's page. I've seen the slides and will be attending this webinar, which looks to have good content.
Good luck! I hope everything turns out OK. There is a high likelihood that everything is fine.