Here are some suggestions of angles which might help to persuade your dh and mum....
Have you investigated / got involved with local home ed activities yet? I was just thinking that maybe if your dh and mum knew what sort of activities were available to your ds they might feel more reassured.
I know my Dad felt a lot better when he realised we would have activities with other families to go to, I think he was worried we would be isolated.
Lots of people join in our local events while their children are pre-school age. We started going to HE things when ds1 was nearly 4, and ds2 who is nearly 3 comes along and joins in everything that ds1 (now 6) does - there are lots of other little ones there too.
Also, you could join a local after school group or meet up regularly with other children you know, so they see that your ds is meeting other children in that way too.
Although in school your ds would probably spend more hours in the company of other children, and come into contact with a greater number in one place, the actual social experience is not necessarily better. In fact the number of different types of social experience / different types of people met may be less.
Or, depending on your ds' personality, it may that the kind of social experiences he can have through home ed would benefit him more - certainly with my ds1 he is much more confident in smaller groups where he can gradually get involved. In the long run I think those sort of experiences are making him far more socially confident and able to be himself - he is only shy and anxious in big, busy, noisy groups which is of course what he would face daily at school.
I'm sure that in time your dh and mum would see that your ds is doing fine socially, but it is hard facing those doubts and staying confident in your decision! Maybe you could suggest to dh that you try HE and then review if he doesn't feel that your ds' social needs are being met - rather than the other way round. We started HE as a "for now" thing but have never looked back.
Good luck with the decision. And if it is any reassurance - the first 2 days of our HE week have been:
Monday - gym lesson with about 15 HE children, followed by park with 3 others from gym class, followed by playing with neighbours children all evening.
Tuesday - swimming lesson with 8 HE children, play in pool after, then playing all afternoon with cousins.
No social interaction there then!