Without knowing the details it seems that the company you are purchasing from are in fact registered for VAT in Ireland otherwise they wouldn't be charging you VAT at the Irish rate but at their local rate. Therefore if you register for Vat you should be able to simply claim the vat back on the purchase from what I can tell.
If it is not the case that they are registered in Ireland the rules is basically the intra-community purchase of goods from a Vat registered person/company from another EU country is deemed to take place where the goods are when the transportation ends. When purchasing the goods you could simply supply them with you Irish Vat registration number for inclusion on their Vat invoice. This will enable the goods to be zero rated in the other EU country (The supplier must have evidence that the goods are leaving the country). Then on acquiring the goods you are required to self account for Vat at the rate appropriate to the goods on your own Vat return. This means that you include the Vat on the goods in both the Vat on sales and Vat on Purchases sections of your Vat return therefore not actually effecting your Vat liability.
An example of this would be say you make a purchase of €1,000 net of Vat. At the moment you are being charged €1,210 by the supplier. If you give them your Vat registration number they will not have to charge you vat and therefore you will only pay them €1,000. Then when you receive the goods a supply of goods has taken place and you will need to return the relevant Vat to the revenue, ie. adding €210 to your Vat on Sales for that period. However as you are using the goods for the purpose of your trade you can also claim the Vat on the Purchase of €210 back, resulting in the goods only costing you €1,000.
Even though it seems pointless including the Vat on your Vat return as it doesn't effect your liability the revenue don't look at it this way and could charge penalties if they found out that it was omitted.
Also, what Karangka said, you cannot charge Vat if you are not Vat registered so you should either refund the Vat to your customers or register for Vat and issue valid Vat invoices (stating your Vat number) to the customers. I would say that seeming as your customers appear to already being willing to pay Vat it would probably be worth your while just registering for VAT.
As for Vat returns, they are not actually that complicated and if you know any accountant that you could sit down with for an hour or two and run through the basics then it wouldn't be too hard to do them on your own. If you're not too confident about doing the returns yourself a way to cut back on costs may be to estimate your monthly Vat liability and sign up for a direct debit Vat payments option. This way you pay a direct debit every month and then at the end of your accounting year you prepare an annual Vat return therefore cuting back on the amount of work you need to do during the year. You could then prepare a draft Vat Return and ask an accountant to review your workings. This way you get the assurance that an accountant considers the return is correct without having to pay him to prepare it. It would depend on the level of transactions involved but I can't imagine that an accountant would charge too much to simply review a return. Say a few hundred €.