There's a few things you can do here:
Important meetings within core hours are highlighted as mandatory.
Tasks are given specific timescales.
Response times are given timescales.
Regular mandatory team meetings within core hours, which could be classed as levelling sessions - gives the team time and space to look at what's working and what isn't and take feedback from them.
Have very clear expectations of what's needed and communicate this to the team.
Essentially, forget about whether they like you or not, be clear in your communications and give the team a voice or platform for their ideas and suggestions and take on board those that would mean continuous improvements are being made.
Ask for further management training by either using the resources available or see if there is scope for someone higher up to mentor you.
Have regular meetings with the team's manager.
Show support to your team and offer a regular meeting to individuals within that support if they ask for it.
Look at the government's "work passport" document and implement something similar. These are owned by the employee and only shared with those they give consent to. These are a wonderful way of starting open communication. They list strengths, support needs and how they work best. If it works for your team, discuss bringing it into the wider business for all. They can highlight reasonable adjustments for those who aren't comfortable disclosing a disability or neuro type as a diagnosis isn't necessary.
I've seen huge differences in team engagement and morale where these have been used.
Take on board constructive feedback, reflect on it and see if they have a point.
And remember, teams will always moan about their manager, as it's the nature of the beast. You can't please all the people all of the time.