Yes - that all sounds right Cheeky! 2 weeks unpaid is a statutory right, even if they cannot pay smp for whatever reason.
I'm pretty sure that you'll get the smp from what you have stated, as your earnings are over the limit by the sounds of it (they'll need to check your earnings for the time between week 15 & week 23 of pregnancy)
So if you hand in matB1 to small employer (ask midwife for new one if you have handed first one over to employer 1) they have to get back to you and either
a) say yes you are entitled to smp from us and we will pay you, or
b) give you an smp1 form which will give you the reason they cannot pay. (So if your earnings were not enough during qualifying weeks or because you have notified them too late, or any other reason.)
Is it a smallish company (the part time one?) I only ask as sometimes the firms themselves struggle to work out whats what with smp - its useful to know the rules in your own situation so you can make sure that your employer has the facts right! if it is a small company they may well be able to claim upfront funding for the smp they pay you - let them have a look at this link - www.hmrc.gov.uk/paye/employees/statutory-pay/funding.htm if you can.
Lastly - no, you don't have to inform HMRC of anything. As you are on paye for both employments all smp will be reported alongside the rest of your earnings for the year in the usual way next April.