Yes and No. You're on dodgy ground as a) it comes down to whether you're eligible (financially speaking) for legal aid (irrespective of whether or not there's abuse). LA is impossible to get unless you're clearly in the criteria, e.g. the abuse is already there before the divorce shenanigans, you're broke, and it's recorded officially.
However, what he's doing is NOT acceptable. Also, I imagine, you feel very sensitive that your children are present so you can't react. That, to my mind, is why the "boundary" is being abused.
What I'd recommend is
a) think about how else handovers can be done (if at all), then ask your solicitor to write to him, using her 'legaltastic' terms to sound authoritative that it can't continue in the current manner and 'decree' how it's going to be going further.
b) If there's no intermediary you could use. Ask her to write that if the verbal abuse/physical contact continues, then it will give you 'no recourse' but to record handovers on your phone, or request witnesses do.
To get a Non-Mol, or any kind of court order, there has to be something to persuade a judge you are turning to him as a last resort. If you're solicitor-led, then it will be after they have tried to mollify him first. Does that make sense.
And also, please, don't entertain 'text nonsense'. Just 'No contact' beyond dates, facts, and times.
Take care.