Do they do any activities with other kids? You could also start with some small classes with other kids where the parents may be present even if not actively involved.
For example, in my area, we have My Gym. The classes are grouped by age and there is some circle time, some free play, and some directed type activities (to try out a new gym-like skill). Some other examples, might be a music related class, art class, or sports (soccer). This gives them some exposure to other children but the parents or care-giver may also be present.
Another thought is to start with a parent-participation type pre-school. These can vary from requiring a lot of work to requiring very little. I have my kids in one requiring only parent involvement on their assigned workdays during class time (and nothing at night or weekends). Their school also lets another non-parent caregiver fulfill the parental obligations, so if you work, you would need to find one that allows your parents, if willing, to fulfill the work obligations. This might provide a way to ease them into it since you or your parents will still be there in the beginning. At the parent participation school we did, the teachers would have the parents leave on their non-work days for small time periods in the beginning until the kids got used to it. They also had discussion times where sometimes the parent was on site but in a different room during the class so the children have other opportunities to be there without their parent/caregiver.
With twins, depending on the school, you may have two work days...or if both your parents can help, maybe you can have them work the same work day and leave the kids as a drop off for the other 1-2 days of pre-school.
I started with a 2-day pre-k when mine were 3 and did a 3 day pre-k now at age 4. Our nanny works one day. The other two days, I drop them off and the nanny picks them up. It has worked well for us. Next year, since they don't meet the age requirements for kindergarten, I will do a full drop off pre-K class.